We provide understanding quadrilaterals practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on understanding quadrilaterals skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of understanding quadrilaterals Questions

Question No | Questions | Class |
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1 | ( A B C D ) is a square of side ( 14 mathrm{cm} . ) Find the radius of the circle. | 8 |

2 | n an isosceles, trapezium ( A B C D, angle C ) is equal to: 45 155 5 3. ( 65^{circ} ) ( c cdot 105 ) 0.75 | 8 |

3 | Given: Parallelogram ( A B C D ) in which diagonal ( A C ) and ( B D ) intersect at ( M ) Prove ( M ) is the mid-point of ( L N ) | 8 |

4 | In the figure, ABCDEF is a regular hexagon, and its centre is point 0. What is the value of ( x ? ) A ( cdot 80^{circ} ) B. ( 60^{circ} ) ( c cdot 40^{circ} ) ( D .30 ) | 8 |

5 | 68. If ABCD is a cyclic parallelo- gram, then the ZA is (1) 100° (2) 60° (3) 80º (4) 90° | 8 |

6 | Draw two angles of ( 90^{circ} ) at the ends of a line segment. Extend these rays. Do you get a triangle. Join these 2 rays by another line segment which shape can yo get? What will be the measure of all the angles? | 8 |

7 | Define a polygon. | 8 |

8 | What is a regular polygon? | 8 |

9 | PQRS is a parallelogram whose diagonals intersect at ( mathrm{M} ) If ( angle P M S=54^{circ}, angle Q S R=25^{circ} ) and ( angle boldsymbol{S} boldsymbol{Q} boldsymbol{R}=boldsymbol{3} boldsymbol{0}^{circ}: ) find ( angle boldsymbol{R} boldsymbol{P} boldsymbol{S} ) A ( .86^{circ} ) B. ( 96^{circ} ) ( c cdot 92^{circ} ) D. ( 100^{circ} ) | 8 |

10 | 10. In the figure given below, PTU is a straight line. What is the value of x? (a) 100 @ 120d (b) 110 ) 130 | 8 |

11 | Find the number of sides of a regular polygon if each exterior angle measures: ( 60^{circ} ) | 8 |

12 | If diagonals of the parallelogram are equal,then show that it is a rectangle. | 8 |

13 | The bisector of any two adjacent angles of a square form an isosceles-rightangled triangle. If the above statement is true then mention answer as 1 , else mention 0 if false | 8 |

14 | In a rectangle ( A B C D ), diagonals intersect at ( 0 . ) If ( angle O A B=30^{circ} ) find: ( angle A C B, angle A B O, angle ) ( mathrm{COD}, angle mathrm{BOC} ) | 8 |

15 | 7. Construct a rhombus PAIR, given that PA=6 cm and angle ZA=110°. | 8 |

16 | In a parallelogram ( A B C D, ) if ( A B= ) ( mathbf{2} boldsymbol{x}+mathbf{5}, boldsymbol{C} boldsymbol{D}=boldsymbol{y}+mathbf{1}, boldsymbol{A} boldsymbol{D}=boldsymbol{y}+mathbf{5} ) and ( B C=3 x-4, ) what is the ratio of ( A B ) and ( B C ? ) A .71: 21 B. 12: 11 c. 31: 35 D. 4: 7 | 8 |

17 | In parallelogram ( A B C D ) the length ( A B ) and ( C D ) are both 4 , the length of diagonal ( A C=4 ) and the length of diagonal ( B D=6 . ) The length ( A D ) equal to A. ( sqrt{10} ) B. ( sqrt{12} ) ( c cdot sqrt{15} ) D. ( sqrt{20} ) | 8 |

18 | 1. In Fig., AB || DC. Find the value of x. | 8 |

19 | A regular polygon is inscribed in a circle. If a side subtends an angle of ( 30^{circ} ) at the centre, what is the number of its sides? A . 10 B. 8 ( c .6 ) D. 12 | 8 |

20 | 11. A lilne lis parallel to line m and a transversal p interesects them at X, Y respectively. Bisectors of interior angles at X and Y intersect at P and Q. Is PXQY a rectangle? Give reason. | 8 |

21 | HOPE is a parallelogram as shown in the given figure. The value of ( y ) is ( mathbf{A} cdot 21^{circ} ) B . ( 14^{circ} ) ( c cdot 35^{circ} ) ( D cdot 27 ) | 8 |

22 | One angle of a six-sided polygon is ( 140^{circ} ) and the other angles are equal. Find the measure of each equal angle. ( mathbf{A} cdot 116^{circ} ) B . ( 130^{circ} ) c. ( 120^{circ} ) D. ( 110^{circ} ) | 8 |

23 | 11. The diagonals of a quadrilateral are of lengths 6 cm and 8 cm. If the diagonals bisect each other at right angles, what is the length of each side of the quadrilateral ? | 8 |

24 | The angles of a convex pentagon are in the ratio ( 2: 3: 5: 9: 11 . ) Find the measure of each angle. | 8 |

25 | 5. In which quadrilateral digonals bisect each other? (a) Parallelogram (b) Rectangle (c) Square (d) Rhombus | 8 |

26 | In a parallelogram ( A B C D, ) the side ( D C ) is produced to ( E ) and ( angle B C E=105^{circ} ) Calculate ( angle A, angle B, angle C, ) and ( angle D ) | 8 |

27 | In the figure given below, ( A B C D ) is a trapezium in which ( A B | D C . E ) and ( F ) are the midpoint of ( A D ) and ( B C ) respectively. ( D F ) and ( A B ) are produced to meet at ( G . ) Also ( A C ) and ( E F ) intersect at point ( O . ) Show that : ( (i) E O | A B ) ( (i) A O=C O ) | 8 |

28 | Say True or False. All the sides of a rhombus are of equal length. A. True B. False | 8 |

29 | Assertion : A polygon bounded by four line segments is called a quadrilateral. Reason: A polygon bounded by seven line segments is called a hexagon Assertion : Anolygon having 16 sides is nolled 16 | 8 |

30 | 12. ABCD is a parallelogram. Points P and Q are taken on the sides AB and AD respectively and the parallelogram PRQA is formed. If ZC=45°, find ZR | 8 |

31 | Two angles of a hexagon are ( 90^{circ} ) and ( 10^{circ} ) remaining four angles are equal find each equal angle. | 8 |

32 | Classify the following curve as open or closed: | 8 |

33 | If in a polygon the number of diagonals is 54 then the number of sides of this polygon is? | 8 |

34 | Two angles of a polygon are right angles and the remaining are ( 120^{circ} ) each. Find the number of sides in it. | 8 |

35 | (a) Is it possible to have a regular polygon with measure of each exterior angle as ( 22^{circ} ? ) (b) Can it be an interior angle of a regular polygon? Why? | 8 |

36 | In the given figure ( overrightarrow{A B} | overrightarrow{D E} ) and area of the parallelogram ABFD is ( 24 c m^{2} ) Find the area of ( Delta A F B ) | 8 |

37 | In the rhombus ( A B C D, A C ) and ( B D ) are the diagonals. If the diagonals are ( 16 mathrm{cm} ) and ( 12 mathrm{cm} . ) Find the length of each of its sides. ( A cdot 10 mathrm{cm} ) B. 12 ( mathrm{cm} ) ( c cdot 9 mathrm{cm} ) D. ( 8 mathrm{cm} ) | 8 |

38 | 9. Find the values of x and y in the following parallelogram. by Find 120 (5x + 1000 | 8 |

39 | 5. Is it possible to construct a quadrilateral ROAM in which RO= 4 cm, OA=5 cm, 20= 120°, ZR= 105º and ZA= 135°? If not, why? | 8 |

40 | ( A B ) and ( C D ) are two vertical poles of height ( 6 m ) and ( 11 m ) respectively. If the distance between their feet is ( 12 m, ) find the distance between their tops. ( mathbf{A} cdot 13 m ) B. ( 5 m ) ( c .11 m ) D. ( 12 m ) | 8 |

41 | If the points ( boldsymbol{P}(mathbf{2}, mathbf{1},-mathbf{3}), boldsymbol{Q}(mathbf{5}, mathbf{4}, mathbf{3}) ) and ( R(1,4,7) ) are three vertices of a parallelogram ( P Q R S ) then the other vertex is A. (1,0,0) В . (-2,1,1) c. (-2,2,1) D. (2,1,2) | 8 |

42 | If the diagonal of a rectangle is twice one of the sides, then the ratio of the sides of the rectangle is A. ( sqrt{2}: 1 ) в. ( sqrt{3}: 1 ) ( c cdot 2 sqrt{2}: 1 ) D. ( 2 sqrt{3}: 1 ) | 8 |

43 | In a parallelogram PQRS, X is the mid point of PS and Y is the mid point of QR, then ( X Y ) divides ( Q S ) in the ratio of A .1: 4 B. 1: 1 c. 1: 2 D. 1: 3 | 8 |

44 | What is true about this figure? A. It is a quadrilateral B. It is a polygon c. It is an octagon D. It is a regular polygon | 8 |

45 | One angle of a seven-sided polygon is ( 114 . ) and each of the other six angles is ( x ) ( 0^{0} ) The value of ( x ) is A ( .114^{circ} ) B . ( 121^{circ} ) ( c cdot 131^{0} ) D. ( 151^{circ} ) | 8 |

46 | 16. Study the figure and answer the following questions. (1) Name a pair of adjacent sides. (ii) How many pairs of opposite sides are these ? (iii) How many pairs of adjacent angles are there? (iv) Name a pair of opposite angles ? (V) How many pairs of opposite angles are there? 17 Thaadionant fimira DORS is a trapezium in which SRIPO | 8 |

47 | Give Reason: A square can be thought of as a special rectangle. | 8 |

48 | Two times the interior angle of a regular polygon is equal to seven times is exterior angle. Find the interior angle of the polygon and the number of sides in ¡t. A. ( 130^{circ} ) and ( n=9 ) B. ( 140^{circ} ) and ( n=9 ) c. ( 160^{circ} ) and ( n=9 ) D. ( 170^{circ} ) and ( n=9 ) | 8 |

49 | ( P Q R S ) is a parallelogram. From the information given in the figure, find the values of ( x ) and ( y ) | 8 |

50 | 6. A mason has made a concrete slab. He needs it to be rectangular. In what way(s) can he make sure that it is rectangular? (a) By measuring each angle (b) By making opposite sides parallel (c) By measuring the lengths of the diagonals (d) All of these | 8 |

51 | A curve which has 2 end points is called an A. closed curve B. simple curve c. open curve D. None of the above | 8 |

52 | ( P R ) and ( Q S ) are two diameters of a circle with center ( O ) such that ( angle P O Q=90 . ) Then the quadrilateral PQRS is a A. rectangle ( c . ) rhombus D. square | 8 |

53 | Area of a rhombus if its vertices are ( (3, ) 0), (4,5),(-1,4) and (-2,-1) taken in order is A . 24. sq. units B. 36 sq. units c. 48 sq. units D. ( 48 sqrt{2} ) sq. units | 8 |

54 | Find the sum of exterior angles ( boldsymbol{x}+boldsymbol{y}+ ) ( boldsymbol{z}+boldsymbol{p}+boldsymbol{q} ) | 8 |

55 | A quadrilateral is a parallelogram if A. opposite angles are equal. B. opposite angles aren’t obtuse, neither acute. c. opposite sides are not equal. D. none | 8 |

56 | PQRS is a parallelogram and diagonals PR and ( $ Q ) bisect at ( 0 . ) If ( P O=3.5 mathrm{cm} ) and ( 0 Q=4.1 mathrm{cm} . ) What is the length of the diagonals? | 8 |

57 | 17. () What is the minimum interior angle possible for a regular polygon? Why? (i) What is the maximum exterior angle possible for a regular polygon? | 8 |

58 | In a parallelogram ( A B C D, ) if ( A B=2 x+5 ) ( mathrm{CD}=mathrm{y}+1, mathrm{AD}=mathrm{y}+5 ) and ( mathrm{BC}=3 mathrm{x}-4 ) then the ratio of AB:BC is A . 71:21 B. 12:11 ( c cdot 31: 35 ) D. 4: 7 | 8 |

59 | If ( A B C D ) is parallelogram. E is mid-point of ( A B ) and ( C E ) bisects ( angle B C D, ) then ( angle D E C ) is A ( cdot 60^{circ} ) В. ( 90^{circ} ) ( c cdot 100^{circ} ) D. 120 | 8 |

60 | If the figure PQRS is a square M is the midpoint of PQ & RM ( perp ) AB. Prove that ( mathrm{RA}=mathrm{RB} ) | 8 |

61 | 1. The ratio between exterior angle and interior angle of regular polygon is 1:5. Find the number of sides of the polygon | 8 |

62 | A rectangle ( P Q R S ) is inscribed in a quadrant of a circle, with ( P ) at the centre and ( R ) on the circumference. If ( P S ) is ( 12 mathrm{cm} ) and ( Q P ) is ( 5 mathrm{cm} ) then the diameter of the circle is ( mathbf{A} cdot 26 mathrm{cm} ) B. ( 29 mathrm{cm} ) ( mathbf{c} .28 mathrm{cm} ) D. none of these | 8 |

63 | The interior of a closed figure has a A. space B. boundary c. diagonal D. None of the above | 8 |

64 | In a trapezium ( A B C D ) with ( A B | C D ) the given that ( A D ) is not parallel to ( B C ) Is ( triangle A B C cong triangle A D C ? ) Give reasons | 8 |

65 | To find the sum of interior angles, we multiply the number of triangles by ( mathbf{A} cdot 360^{circ} ) B. ( 120^{circ} ) ( c cdot 180^{circ} ) D. ( 240^{circ} ) | 8 |

66 | ( A B C D ) is a rhombus such that ( angle A D B=50^{circ}, ) then what is the measure of ( angle A C B ? ) | 8 |

67 | Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with: (i) 7 sides (ii) 10 sides (iii) 250 sides | 8 |

68 | 8. The diagonals of a rectangle bisect each other at right angles. ana hisect each other at right angles. | 8 |

69 | Is it possible to have a regular polygon whose each interior angle is ( 170^{circ} ) State true or false: A. True B. False | 8 |

70 | What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides | 8 |

71 | 1. The ratio of two sides of a parallelogram is 4 : 3 and its perimeter is 56 m. If the sides of parallelogram be a and b. atb Then is | 8 |

72 | The perimeter of a parallelogram,whose one side measures 12 inches, is 72 inches. Find the length of its other three sides. A. 12,12,36 B. 12, 18, 18 c. 12,24,24 D. 12,30,30 | 8 |

73 | 3. Some rectangles are also squares. | 8 |

74 | Sum of interior angle of quadrilateral equals A . ( 300^{circ} ) B. ( 180^{circ} ) ( c .360^{circ} ) D. ( 540^{circ} ) | 8 |

75 | Fill in the blank All squares are (similar, congruent) A. similar B. congruent c. Undefined D. None of these | 8 |

76 | 3. The bisectors of angles of a parallelogram enclose a S (a) Rhombus (c) Square (b) Rectangle (d) Parallelogram TI | 8 |

77 | There is a regular polygon whose each interior angle is ( 145^{circ} ) State true or false. A. True B. False | 8 |

78 | The straight line ( A B ) is divided at ( C ) so that ( A C=3 C B . ) Circles are described on ( A C ) and ( C B ) as diameters and a common tangent meets AB produced at D. Then ( B D ) equals. A. the diameter of the smaller circle B. the radius of the smaller circle c. the radius of the larger circle D. ( overline{C B} sqrt{3} ) E. the difference of the two radi | 8 |

79 | How many diagonals are there in a hexagon? A. 6 B. 4 ( c cdot 11 ) ( D ) | 8 |

80 | State true or false. Is it possible to have a regular polygon whose each exterior angle is ( 32^{circ} ) A. True B. False | 8 |

81 | In a rectangle ( A B C D, A B=12 mathrm{cm} ) and ( angle B A C=30^{circ} . ) Calculate the length of side ( B C ) and diagonal ( A C ) | 8 |

82 | ABCD is a rhombus whose one angle is 60′. The ratio the lengths of its diagonals is (a) 3:1 (b) 2:1 (c) 2:1 (d) 3:1 | 8 |

83 | Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) What can you say about the angle sum of a convex polygon with number of sides? | 8 |

84 | In a trapezium ( A B C D, ) side ( A B ) is parallel to side ( mathrm{DC} ; ) and the diagonals ( mathrm{AC} ) and ( mathrm{BD} ) intersect each other at a point Such that: ( boldsymbol{P A} times boldsymbol{P D}=boldsymbol{P B} times boldsymbol{P C} ) A. True B. False | 8 |

85 | 2. In Fig, find the measure of ZMPN. OU M | 8 |

86 | Find the number of diagonals of a polygon of 16 sides. | 8 |

87 | In the adjoining figure, ( A B C D ) is a trapezium in which ( A B ) DC and ( A D=B C . ) If ( P, Q, R, S ) be | 8 |

88 | The diagonals of a rectangle ( A B C D ) intersect each other in ( O . ) If angle ( A O D ) is ( 30^{0}, ) then find angle ( O C D ) | 8 |

89 | 1. How many diagonals does each of the following have? ( A convex quadrilateral (ii) A regular hexagon (i) A triangle | 8 |

90 | What is a curve? A. A line which is not straight and does not any sharp edges B. It is a polygon C . It is a quadrilateral D. A line with sharp edges. | 8 |

91 | 13. In the following figure, FD || BC || AE and AC || ED. Find the value of x. 5640 n . 1 | 8 |

92 | Classify the given curves are (i) Open or (ii) Closed. | 8 |

93 | How many sides does a regular polygon has if each of it’s interior angle is ( 120^{circ} ? ) | 8 |

94 | State true or false: Is it possible to have a polygon whose sum of interior angles is ( 540^{circ} ? ) A. True B. False | 8 |

95 | ABCD is a trapezium in which ( boldsymbol{A B} | ) ( boldsymbol{D} boldsymbol{C}, boldsymbol{A B}=mathbf{5 0} mathrm{cm}, boldsymbol{D} boldsymbol{C}=mathbf{3 0} mathrm{cm} . ) If ( boldsymbol{X} ) and ( Y ) are respectively the mid-points of ( A D ) and ( B C, ) prove that ( boldsymbol{a} boldsymbol{r}(operatorname{trap} cdot boldsymbol{D} boldsymbol{C} boldsymbol{Y} boldsymbol{X})= ) ( frac{mathbf{7}}{mathbf{9}} boldsymbol{a} boldsymbol{r}(operatorname{trap} . boldsymbol{X} boldsymbol{Y} boldsymbol{B} boldsymbol{A}) ) | 8 |

96 | If ( A(-2,-1), B(a, 0), C(4, b) ) and ( D(1,2) ) are the vertices of a parallelogram, find the values of a and b. | 8 |

97 | 8. In figure, RENT is a rectangle. Its diagonals meet at O. Find x. ifOR=2x + 4 and OT=3x + 1. 3x + 1 2x+4 | 8 |

98 | Which of the following is different from the other three? ( mathbf{A} ) ( B ) ( mathbf{C} ) D. | 8 |

99 | ITSUMUTULUI0IU OUT 6. 7 In a parallelohram opposite angles are not equal. Ferrhombuis kite | 8 |

100 | The radius of a circles ( 17 mathrm{cm} ) and the length of one of its chord is ( 16 mathrm{cm} ). Find the distance of the chord from the centre | 8 |

101 | Find ( (x, y) ) if ( (3,2),(6,3),(x, y) ) and (6,5) are the vertices of a parallelogram A . (9,6) B. (6,6) ( c .(9,9) ) D. None of these | 8 |

102 | ES 120° 11. 70° IC In the above figure both RISK and CLUE are parallelograms. Find the value of x. Cindthemen.nf and Zsif SPRO in Fig (If you | 8 |

103 | Assertion : The adjacent angles in a parallelogram are supplementary, Reason: In a parallelogram, the adjacent angles are always equal. | 8 |

104 | The exterior angle of a regular polygon is ( 24^{circ} ) Find the number of sides of this regular polygon. | 8 |

105 | In a regular pentagon ( A B C D E ; A C ) and ( B E ) intersect at ( P . ) Calculate the angles ( C B E ) and ( B P A ) ( A cdot 30^{circ} ) and ( 60^{circ} ) B. ( 72^{circ} ) and ( 108^{circ} ) c. ( 54^{circ} ) and ( 108^{circ} ) D. ( 72^{circ} ) and ( 72^{circ} ) | 8 |

106 | Let ( F_{1} ) be the set all of parallelograms, ( F_{2} ) be the set of the rectangles, ( F_{3} ) be the set of rhombuses, ( F_{4} ) be the set of squares ( F_{5} ) be the set of trapezium in a plane then ( F_{1}= ) A. ( F_{2} cap F_{3} ) B. ( F_{2} cup F_{3} cup F_{4} ) c. ( F_{3} cup F_{4} cup F_{5} ) D. ( F_{3} cap F_{1} ) | 8 |

107 | If the sides ( A B, B C, C D ) and ( D A ) of a trapezium ABCD measure ( 10 mathrm{cm}, 20 mathrm{cm} ) ( 18 mathrm{cm} ) and ( 16 mathrm{cm} ) respectively then find the length of the longer diagonal given that ( A B ) is parallel to ( C D ) A ( . sqrt{760} mathrm{cm} ) В. ( sqrt{231} mathrm{cm} ) ( c cdot sqrt{54} c m ) D. ( sqrt{930} mathrm{cm} ) | 8 |

108 | If non parallel sides of a trapezium are equal, prove that it is cyclic. | 8 |

109 | Polygons are figures. A. many sided B. one sided c. has no sides D. two sides | 8 |

110 | In the figure at right, ( A B C D ) is a parallelogram ( angle B A O= ) ( mathbf{3 0}^{circ}, angle boldsymbol{D A O}=angle mathbf{4 5}^{circ} ) and ( angle boldsymbol{C O D}= ) ( mathbf{1 0 5}^{circ} . ) Calculate ( angle C B D ) A ( cdot 60^{circ} ) B. 30 ( c cdot 20 ) D. None of these | 8 |

111 | The interior angles of a polygon are in arithmetic progression. The smallest angle is ( 120^{circ} ) and the common difference is ( 5 . ) Find the number of sides of the polygon. | 8 |

112 | 7. In trapezium HARE, EP and RP are bisectors of Z E and Rrespectively. Find Z HAR and ZEHA. ER250 30° P 15. | 8 |

113 | In ancient India, the shapes of altars used for house hold rituals were A. squares and circles B. triangles and rectangles c. trapeziums and pyramids D. rectangles and squares | 8 |

114 | 4. All squares and rectangles are also parallelograms. Tf1 1: 1 ito luas as | 8 |

115 | Calculate the sum of angles of a polygon having 10 sides. A ( .960^{circ} ) B. ( 1440^{circ} ) c. ( 900^{circ} ) D. 720 | 8 |

116 | B 6. In a parallelogram ABCD, the bisectors of Z A and meet at O. Find ZAOB. | 8 |

117 | Explain how square is a quadrilateral. A. All angles are equal B. Because it is four sided c. Two sides are equal D. None of these | 8 |

118 | n quadrilateral ABCD ( angle mathrm{B}=90^{circ}, angle mathrm{C}-angle ) ( mathrm{D}=mathbf{6 0}^{circ} ) and ( angle mathbf{A}-angle mathbf{C}-angle mathbf{D}=mathbf{1 0}^{circ} . ) Find ( A, angle C ) and ( angle D ) | 8 |

119 | The diagonals ( A C ) and ( B D ) of a parallelogram ( A B C D ) intersect each other at the point ( O ) If ( angle D A C=32^{circ} ) and ( angle A O B=70^{circ}, ) then ( angle D B C ) is equal to? A ( cdot 24^{circ} ) B. ( 86^{circ} ) ( c cdot 38^{circ} ) ( D cdot 32^{circ} ) | 8 |

120 | One of the diagonals of a rhombus is equal to a side of the rhombus. The angles of the rhombus are ( mathbf{A} cdot 60^{circ} a n d 80^{circ} ) B ( cdot 60^{circ} ) and ( 120^{circ} ) c. ( 120^{circ} ) and ( 240^{circ} ) D. ( 100^{circ} ) and ( 120^{circ} ) | 8 |

121 | 5. In a quadrilateral ABCD, ZB = 90° and AD2 = AB2 + BC2 + CD2 then ZACD is equal to (a) 90° (b) 60° (c) 30° (d) None of these | 8 |

122 | .has the same properties of that of a rhombus but not a rectangle. A. Square B. Parallelogram c. Trapezium D. Kite | 8 |

123 | The difference between an interior angle of ( (n-1) ) sided regular polygon and an interior angle of ( (n+1) ) sided regular polygon is ( 9^{circ} . ) Find the value of ( n ) ( A cdot 3 ) B. 4 ( c .9 ) D. 12 | 8 |

124 | In the following figure, ABCD to a trapezium with ( A B | D C ). If ( A B=9 mathrm{cm}, D C= ) ( 18 mathrm{cm}, mathrm{CF}=13.5 mathrm{cm}, mathrm{AP}=6 mathrm{cm} ) and BE=15 cm. Calculate PE ( A cdot P E=5.8 mathrm{cm} ) 3. ( P E=4.8 mathrm{cm} ) ( c cdot P E=2.8 mathrm{cm} ) ( P E=3.8 mathrm{cm} ) | 8 |

125 | Find the area of ( square A B C D ) ( mathbf{A} cdot 4(24+25 sqrt{3}) c m^{2} ) B ( cdot 4(25+24 sqrt{3}) c m^{2} ) ( mathbf{c} cdot 2(24+25 sqrt{3}) c m^{2} ) D. None of these | 8 |

126 | Find ( x ) | 8 |

127 | ( A B C D ) and ( P Q R C ) are rectangle where ( Q ) is the mid-point of ( A C . ) Prove that ( boldsymbol{D} boldsymbol{P}=boldsymbol{P C} ) | 8 |

128 | ( A B C ) is a right-angled triangle and 0 is the mid point of the side opposite to the right angle. Explain why 0 is equidistant from ( A, B ) and ( C ) (The dotted lines are drawn additionally to help you) | 8 |

129 | In a trapezium ( mathrm{ABCD}, mathrm{AB}|| mathrm{CD} . ) If ( angle boldsymbol{A}= ) ( 60^{circ} ) then ( angle D=? ) A ( .100^{circ} ) B. ( 120^{circ} ) ( c cdot 70 ) D. 300 | 8 |

130 | State true or false: The bisector of any two adjacent angles of a rhombus form a right-angled triangle. A. True B. False | 8 |

131 | ( A B C D ) is a rhombus with ( angle A B C= ) ( 56^{circ}, ) then ( angle A C B ) will be A ( .56^{circ} ) B. ( 124^{circ} ) ( c cdot 62^{0} ) D. ( 34^{circ} ) | 8 |

132 | n the figure, two identical regular hexagons are placed side by side as shown, then find the value of z. A ( cdot 60^{circ} ) В. ( 90^{circ} ) ( c cdot 120^{circ} ) D. ( 160^{circ} ) | 8 |

133 | Three angles of a seven sided polygon are ( 132^{circ} ) each and the remaining four angles are equal. Find the value of each equal angle. A .125 B. ( 156^{circ} ) ( c cdot 126^{circ} ) D. ( 130^{circ} ) | 8 |

134 | In a polygon, there are 5 right angles and the remaining angles are equal to ( mathbf{1 9 5}^{circ} ) each. Find the number of sides in the polygon. A . 5 B. 11 c. 8 D. 7 | 8 |

135 | Points ( X ) and ( Y ) are taken on the sides QR and RS, respectively of a parallelogram PQRS, so that ( Q X=4 X R ) sand ( mathrm{RY}=4 mathrm{YS} ). The line ( mathrm{XY} ) cuts the line PR at Z. Find the ratio PZ:ZR. ( mathbf{A} cdot 4: 21 ) в. 3: 4 c. 21: 4 D. 4: 3 | 8 |

136 | Diagonals ( boldsymbol{A C} ) and ( boldsymbol{B D} ) of a trapezium ( boldsymbol{A B C D} ) with ( boldsymbol{A B} | boldsymbol{D C} ) intersect each other at ( O . ) Prove that ( boldsymbol{a} boldsymbol{r}(boldsymbol{A O D})=boldsymbol{a r}(boldsymbol{B O C}) ) | 8 |

137 | How many diagonals does each of the following have? (a) A convex quadrilateral (b) A regular hexagon (c) A triangle | 8 |

138 | In a polygon, there are 5 right angles and the remaining angles are equal to ( 195^{circ} ) each., Find the number of sides in the polygon. | 8 |

139 | 19 NL, Wily Construct a trapezium ABCD where AB | CD, AD = BC=3.2 cm, AB=6.4 cm and CD=9.6 cm. Measure B and ZA. 6.4 cm A 3.2 cm 3.2 cm 13.2 cm 1600 D4 9.6 cm [Hint : Difference oftwo parallel sides given an equilateral triangle.] | 8 |

140 | In the circle with centre ( boldsymbol{O}, boldsymbol{P Q} ) and ( boldsymbol{R S} ) are diameters. ( M ) and ( N ) are points on the arcs ( Q R ) and ( Q S ) respectively and ( boldsymbol{R} boldsymbol{X}=boldsymbol{S} boldsymbol{Y} ) then ( boldsymbol{P} boldsymbol{X} boldsymbol{Q} boldsymbol{Y} ) is a parallelogram. A. True B. False | 8 |

141 | 58. If ABCD is a parallelogram in which ZA = 60°, AB = 5 cm, BC = 4 cm and the bisectors of ZA and LB meet at point P lying on side CD, then what will be the value of PD? (1) 4 cm (2) 5 cm (3) 3 cm (4) 6 cm | 8 |

142 | Find the fourth vertex of the parallelogram whose consecutive vertices are (8,4),(5,7),(-1,1) | 8 |

143 | ( P Q, Q R ) and ( R S ) are three consecutive sides of a regular polygon. If ( <Q P R= ) ( 20^{circ} ) find the number of side in the polygon. | 8 |

144 | 10. Find measure.x. 9001 500 110° 1 Lat PORS hea rhombus find y | 8 |

145 | ( A B=D C=8 c m, A D=4 c m ) what should be the length of side ( B C ), if ( A B C D ) is parallelogram A. ( 4 c m ) B. 8 cm ( mathbf{c} cdot 16 c m ) D. None of the above | 8 |

146 | Number of diagonals in parallelogram is/are: A. 0 B. ( c cdot 2 ) D. none of these | 8 |

147 | The diagonals of a parallelogram ( A B C D ) intersect at ( O . A ) line through intersect ( A B ) at ( X ) and ( D C ) at ( Y ). Identify the correct option A. ( O X=O Y ) в. ( O X>O Y ) c. ( O X<O Y ) ( cdot O X-O Y=0 ) 0 | 8 |

148 | The figure obtained by joining the midpoints of the sides of a rhombus taken in order is A . a square B. a rhombus c. a rectangle D. parallelogram | 8 |

149 | ( A B C D ) is a rectangle in which diagonal ( B D ) bisects ( angle B . ) Show that ( A B C D ) is a square. | 8 |

150 | In the given figure, ( P Q R S ) is a square and ( angle B A C=90^{circ} . ) Prove that ( : R S^{2}= ) BRxSC | 8 |

151 | Find area of trapezium whose parallel sides ( 9 mathrm{cm} ) and ( 5 mathrm{cm} ) respectively and the distance between these sides is ( mathbf{8} c boldsymbol{m} ) | 8 |

152 | 15. Explain how the following figure is a trapezium? Which of its two sides are parallel ? 100.90 802 | 8 |

153 | 55. The radius and the height of a cone are in the ratio 4: 3. The ratio of the curved surface area and total surface area of the cone (1) 5:9 (3) 5:4 (2) 3:7 (4) 16:9 | 8 |

154 | 2. In the given figure, ABCD is a quadrilateral and ZADC = “. ZBCD=bº. AO and BO are bisectors of ZDAB and ZABC respectively meeting at O. Find ZAOB in terms of aand b. DO | 8 |

155 | Find the number of sides of a regular polygon if each interior angle is ( 135^{circ} ) | 8 |

156 | The radius of the locus by the point represented by ( z, ) when ( arg frac{z-1}{z+1}=frac{pi}{4} ) is A ( cdot sqrt{2} ) B. ( sqrt{2} pi ) c. ( frac{pi}{sqrt{2}} ) D. none of these | 8 |

157 | Say True or False. All the sides of a parallelogram are of equal length. A. True B. False | 8 |

158 | ( A B C D ) is a trapezium in which ( A B | ) ( D C, A B=16 mathrm{cm} ) and ( D C=24 mathrm{cm} . ) If ( E ) and ( F ) are respectively the midpoints of ( A D ) and ( B C, ) then ( a r(A B F E)= ) ( frac{9}{11} a r(E F C D) ) A . True B. False | 8 |

159 | One angle of a seven sided polygon is ( 108^{circ} ) and each of the other six angles is ( x^{circ} . ) The value of ( x ) is ( mathbf{A} cdot 114^{circ} ) B. ( 121^{circ} ) ( mathrm{c} cdot 131^{circ} ) D. ( 132^{circ} ) | 8 |

160 | The ratio of the area of a square to that of the square drawn on its diagonal is? A . 1: B. 2: c. 1: 2 D. 1: 4 | 8 |

161 | Find the area of a rhombus, each side of which measures ( 20 mathrm{cm} ) and one of whose diagonals is ( 24 mathrm{cm} ) | 8 |

162 | ( A B C ) is a right angled triangle and 0 is the mid point of the side opposite to the right angle. Explain why ( O ) is equidistant from ( A, B ) and, ( C ) | 8 |

163 | 3. In the following figure RISK and CLUE are parallelograms. Then the measure of x is 10kº. Find the value of k. К . E SU 120° 700 I C | 8 |

164 | Find the area of a rhombus if its vertices are (3,0),(4,5),(-1,4) and (-2,-1) taken in order | 8 |

165 | A parallelogram is cut by two set of ( boldsymbol{m} ) lines parallel to its sides. The number of parallelogram thus force is A ( cdotleft(^{m} C_{2}right)^{2} ) B. ( left(^{m+1} C_{2}right)^{2} ) ( mathbf{c} cdotleft(^{m+2} C_{2}right)^{2} ) D. ( m+1 C_{2} ) | 8 |

166 | A ( ldots . . . . . . . . . . . . ) has 4 sides equal and 4 right angles. A . square B. parallelogram c. trapezium D. rectangle | 8 |

167 | Position of P is A. Interior of curve B. Exterior of curve c. on the curve D. can not be said | 8 |

168 | PQRS is a square E and F are points on the sides ( Q R ) and ( R S ) respectively show that ( boldsymbol{a r}(boldsymbol{Delta} boldsymbol{P Q} boldsymbol{E})=boldsymbol{a r}(boldsymbol{Delta} boldsymbol{P S F}) ) | 8 |

169 | How many sides does a Decagon have? A. 7 B. 8 ( c cdot 9 ) D. 10 | 8 |

170 | If the straight line ( x cos alpha+y sin alpha= ) ( p ) touches the curve ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1, ) then prove that ( boldsymbol{a}^{2} cos ^{2} boldsymbol{alpha}+boldsymbol{b}^{2} sin ^{2} boldsymbol{alpha}=boldsymbol{p}^{2} ) | 8 |

171 | 1. All squares are also rectangles. | 8 |

172 | 2. If ZBCD=120°, then _BAD= (a) 60° (b) 120 (c) 180° (d) none of these | 8 |

173 | Points ( P ) and ( Q ) have been taken on opposite sides ( A B ) and ( C D ) respectively of a parallelogram ( A B C D ) such that ( A P=C Q . ) Show that ( A C ) and ( P Q ) disect each other. | 8 |

174 | 56. A parallelogram ABCD has sides AB = 24 cm and AD = 16 cm. The distance between the sides AB and DC is 10 cm. Find the distance between the sides AD and BC. (1) 16 cm (2) 18 cm. (3) 15 cm. (4) 26 cm. | 8 |

175 | The number of triangles are less than the number of sides formed by the diagonals from one vertex. ( A cdot 3 ) B. 5 ( c cdot 8 ) D. | 8 |

176 | Which of the following properties are not true for a parallelogram? (a) Its diagonals are equal. (b) Its diagonals are perpendicular to each other. © The diagonals divide the figure into four congruent triangles. (d) Each diagonal divides a parallelogram into two congruent triangles. | 8 |

177 | 17. The adjacent figure PQRS is a trapezium in which SP ||RQ, find the measures of ZP and ZR. So 6. | 8 |

178 | In given figure ( A B C D ) is a rhombus. If ( angle B A C=38^{circ}, ) find: ( angle A D C ) | 8 |

179 | State true or false: ( A B C D ) is a parallelogram. ( P ) and ( Q ) are the mid-points of sides ( A B ) and ( A D ) respectively. Hence, area of triangle ( A P Q=frac{1}{8} ) of the area of parallelogram ( A B C D ) A. True B. False | 8 |

180 | Which statement is true about the figure formed by joining the midpoints of the adjacent sides of a rectangle with ( operatorname{sides} 8 c m ) and ( 6 c m ? ) A . It is a rectangle of area ( 24 mathrm{cm}^{2} ) B. It is a square of area ( 24 mathrm{cm}^{2} ) C. It is a trapezium of area ( 24 mathrm{cm}^{2} ) P. It is a rhombus of area ( 24 mathrm{cm}^{2} ) | 8 |

181 | If the sum of adjacent angles of a quadrilateral is equal to ( 180^{circ}, ) then quadrilateral is A . a parallelogram B. connex c. concave D. none of the above | 8 |

182 | The ratio of two adjacent sides of a parallelogram is 2: 3 and its perimeter is ( 50 mathrm{cm} . ) Find its area if altitude corresponding to large side is ( 10 mathrm{cm} ) | 8 |

183 | angles. The diagonals of a square bisect each other at right angles. 9. | 8 |

184 | The ratio of two sides of parallelogram is 3: 5 and its perimeter is ( 48 mathrm{cm} . ) Find the sides of the parallelogram | 8 |

185 | Let ( A B C D ) is a square with sides of unit length.Points E and F are taken on ( operatorname{sides} A B ) and ( A D ) respectively so that ( A E=A F ).Let ( P ) be a point inside the ( square A B C D ) Let a line passing through point ( boldsymbol{A} ) divides the square ( square A B C D ) into two parts so that area of one portion is double the other, then the length of portion of line inside the square is A. ( frac{sqrt{10}}{3} ) B. ( frac{sqrt{13}}{3} ) c. ( frac{sqrt{11}}{3} ) D. ( frac{2}{sqrt{3}} ) | 8 |

186 | If ABCD is a parallelogram in which and ( Q ) are the centroids of ( Delta A B D ) and ( Delta B C D, ) then, PQ equals: ( A cdot A Q ) B. AP c. ВР D. DQ | 8 |

187 | Sum of measures of angles of a Nonagon is ( 1260^{circ} . ) Find how much each angle is measured. A ( cdot 100^{circ} ) B . ( 140^{circ} ) ( c cdot 108^{circ} ) D. ( 90^{circ} ) | 8 |

188 | Sum of the interior angles of a regular polygon is ( 1620^{circ} . ) How many sides does this polygon have? | 8 |

189 | ( A B, B C ) and ( C D ) are the three consecutive sides of a regular polygon. If ( angle B A C= ) ( 15^{circ} . ) Find each interior angle of the polygon. A ( .147^{circ} ) B. 162 ( c cdot 150 ) D. ( 140^{circ} ) | 8 |

190 | If the sum of measures of two angles of a hexagon is ( 220^{circ}, ) then what is the sum of the measures of other four angles? A . ( 800^{circ} ) B. ( 700^{circ} ) ( c cdot 600^{circ} ) D. ( 500^{circ} ) | 8 |

191 | A quadrilateral whose all sides are equal and has four right angles is called ( a ) A. rectangle B. rhombus c. kite D. square | 8 |

192 | 8. If in the adjoining figure, ADE and CBF are straight lines, then x not equal to D550 – 65° HBrown A 60°y Porno (a) 55º. (c) 650 (b) 60° s (d) 50° ed | 8 |

193 | ( A B C D ) is a trapezium in which ( A B|| D C ) and its diagonals intersect each other at point ( ^{prime} boldsymbol{O}^{prime} ). Show that ( frac{A O}{B O}=frac{C O}{D O} ) | 8 |

194 | Show that if the diagonal of a quadrilateral bisect each other at right angles,then it is a rhombus | 8 |

195 | If all the angles of a 14 -sided figure are equal, then the measure of each angle is equal to? ( ^{A} cdotleft(184 frac{2}{7}right)^{circ} ) B. ( left(164 frac{2}{7}right) ) ( ^{c} cdotleft(134 frac{2}{7}right)^{circ} ) ( ^{mathrm{D}} cdotleft(154 frac{2}{7}right) ) | 8 |

196 | 1. Find the sum of interior angles of (1) a polygon with 12 sides. (ii) a polygon with 18 sides. Doch interior angle of remular noloon is 1440 Find | 8 |

197 | A square is a A. kite B. trapezium C . triangle D. rhombus | 8 |

198 | ITU MUTUICdSUIC UTCdnUI C U15″ 9. The following figures GUNS and RUNS are rarallelograms. Find x and y: (Length are in cm) 26 واG 3y – 1 + x y 91 + 7 | 8 |

199 | The perimeter of a parallelogram is 150 ( mathrm{cm} ) and one of its side is greater than the other by ( 25 mathrm{cm} . ) Find the lengths of all the sides of that parallelogram | 8 |

200 | In the following figure, ( A B C D ) is a rhombus and ( D C E F ) is a square. If ( angle A B C=56^{circ} ), find ( angle D A E ) ( angle boldsymbol{F} boldsymbol{E} boldsymbol{A} ) ( angle E A C ) ( angle A E C ) + Option | 8 |

201 | If the diagonals of a quadrilateral are perpendicular to each other, the figure would always be included under the general classification: A. rhombus B. rectangle c. square D. isosceles trapezoid E. none of these | 8 |

202 | The difference between an exterior angle of ( (n-1) ) sided regular polygon and an exterior angle of ( (n+2) ) sided regular polygon is ( 6^{circ} . ) Find the value of ( n ) ( A cdot 13 ) B. 12 ( c cdot 16 ) D. 18 | 8 |

203 | ( A B C D ) is a rectangle ( A C ) is diagonal Find the angles of ( triangle A C D . ) Give reasons | 8 |

204 | 1. To construct a parallelogram, the minimum number of measurements required is: (a) 2 (b) 3 (d) 1 (c) 4 | 8 |

205 | In the fig, ( square P Q R S ) and ( square A B C R ) are two parallelograms. f ( angle P=110^{circ} ) then find the measures of all angles of ( square A B C R ) | 8 |

206 | In the figure, ( A B C D ) is a rectangle, ( triangle C E F ) is an equilateral triangle. Find ( x ) A ( cdot 25^{circ} ) B. ( 30^{circ} ) ( c cdot 20^{circ} ) 0.50 | 8 |

207 | 2. Assertion : In all cases of quadrilateral, it is convenient and helpful to draw rough sktech of the quadrilateral and indicate the data on it. Reason : This suggest the steps of construction. | 8 |

208 | Each interior angle of a ( n ) -sided regular polygon is ( 162^{circ} . ) Find the interior angle of another polygon with ( 2 n ) sides. A . ( 155^{circ} ) B . ( 160^{circ} ) ( c cdot 171 ) D. one of the above | 8 |

209 | Fill in the blanks using the correct word given in brackets: Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are ( ldots ) proportional). | 8 |

210 | Which of the following is not the property of a square? A. Each angle of a square is a right angle B. The diagonals of a square are not equal C. The sides of a square are equal D. The diagonals of a square bisect each other right angle | 8 |

211 | 4. A rhombus has all its sides of | 8 |

212 | Find the area of the figure bounded by the following curves ( y=sin x_{2}, y=2 x / pi ) | 8 |

213 | 1. In Fig. PQRS is a square. Determine ZSRP. | 8 |

214 | Ina parallelogram ( A B C D ) the bisector of ( angle A ) also bisects ( B C ) at ( X . ) prove that ( A D=2 A B ) | 8 |

215 | ( A B C D ) is a parallelogram, ( A E ) is perpendicular to ( D C, ) If ( D C=20 mathrm{cm} ) ( A D=5 mathrm{cm} ) and the area of the parallelogram is ( 40 mathrm{cm}^{2} ). Find ( D E ) | 8 |

216 | The sides BA and DC of quadrilateral ABCD are produced as shown in the figure given below. Then x + y is equal to CF aº E A (a) a+b (b) a-b (0) (d) | 8 |

217 | One side of a parallelogram is ( frac{3}{4} ) times its adjacent side. If the perimeter of the parallelogram is ( 70 mathrm{cm}, ) find the sides of the parallelogram. | 8 |

218 | B 15. Consider the following parallelograms. Find the values of the unknown x, y, z. Dy 0001 30 (iv) 800 1129 | 8 |

219 | In the given isosceles trapezium ABCD, ( boldsymbol{A B} | boldsymbol{D C} ) and ( boldsymbol{A D}=boldsymbol{B C} ). If ( angle boldsymbol{D}= ) ( 60^{circ}, A B=18 c m ) and ( A D=12 c m, ) find the length of DC A . ( 60^{circ} ) B. ( 30^{circ} ) ( c cdot 90 ) D. ( 20^{circ} ) | 8 |

220 | 14. In the following figure, AB || DC and AD = BC. Find the value of x. 20 cm 10 cm 60° JB -x cm- | 8 |

221 | In the given figure, ( A B C D ) is a rhombus in which ( angle B C D=110^{circ}, ) find ( (x+y) ) | 8 |

222 | Diagonals ( A C ) and ( B D ) of a parallelogram ABCD intersect each other at ( 0 . ) If ( O A=3 mathrm{cm} ) and ( O D=2 mathrm{cm} ) determine the lengths of ( A C ) and ( B D ) | 8 |

223 | The four angles of a quadrilateral are equal. Draw this quadrilateral in your notebook. Find each of them. A. ( 60^{circ}, 120^{circ}, 30^{circ}, 150^{circ} ) ( ^{circ} ) B. ( 60^{circ}, 120^{circ}, 60^{circ}, 120^{circ} ) ( mathbf{c} cdot 90^{circ}, 90^{circ}, 90^{circ}, 90^{circ} ) D. ( 60^{circ}, 60^{circ}, 120^{circ}, 120^{circ} ) | 8 |

224 | In the given figure, ( A B | ) DC Prove that(i) ( triangle D M U sim triangle B M V(text { ii) } D M times B V= ) ( boldsymbol{B} boldsymbol{M} times boldsymbol{D} boldsymbol{U} ) | 8 |

225 | Vertices of a parallelogram ( A B C D ) are ( boldsymbol{A}(mathbf{3}, mathbf{1}), boldsymbol{B}(mathbf{1 3}, mathbf{6}), boldsymbol{C}(mathbf{1 3}, mathbf{2 1}) ) and ( D(3,16) . ) If a line passing through the origin divides the parallelogram into two congruent parts then the slope of the line is A ( cdot frac{11}{12} ) в. ( frac{11}{8} ) c. ( frac{25}{8} ) D. ( frac{13}{8} ) | 8 |

226 | State whether the following statements are true of false Circles with same radii are equal A. True B. False | 8 |

227 | The measures of two complements are ( x ) and ( (x+50)^{circ} . ) Find the measure of each of them | 8 |

228 | Polygons that have any portions of their diagonals in their exterior are called A. squares B. convex polygons c. concave polygons D. triangles | 8 |

229 | Find the number of sides of a regular polygon if each exterior angle is equal to one third of its adjacent interior angle | 8 |

230 | Prove that a diagonals of a parallelogram divides it into two congruent triangles. | 8 |

231 | The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are ( (6 x-1)^{circ},(10 x+ ) 2) ( ^{circ},(8 x+2)^{circ},(9 x-3)^{circ},(5 x+4)^{circ} ) and ( (12 x+6)^{circ} ; ) Find each exterior angle B . ( 41^{circ}, 86^{circ}, 56^{circ}, 60^{circ}, 39^{circ}, 80^{circ} ) C ( cdot 41^{circ}, 72^{circ}, 58^{circ}, 60^{circ}, 39^{circ}, 90^{circ} ) D. ( 41^{circ}, 82^{circ}, 60^{circ}, 60^{circ}, 36^{circ}, 100 ) | 8 |

232 | In the following figure, ABCD is a parallelogram and EFCD is a rectangle. Also, ( A L perp D C . ) Prove that (i) ( operatorname{ar}(mathrm{ABCD})=operatorname{ar}(mathrm{EFCD}) ) (ii) ( operatorname{ar}(mathrm{ABCD})=mathrm{DC} times mathrm{AL} ) | 8 |

233 | 5. 6. yuu alu Teulallgles are also paralluogo. If the diagonals of a rhombus are equal, its always a square. In a parallelohram opposite angles are not equal | 8 |

234 | In square PQRS. if ( mathrm{PQ}=3 x-7 ) and ( Q R=x+3 ; ) find PS ( A cdot 6 ) B. 7 ( c cdot 8 ) D. 5 | 8 |

235 | In the figure(not drawn to scale), ABCD is a rhombus, ABE is a straight line. Find ( angle mathrm{DBE} ) A . 150 B. ( 152^{circ} ) ( mathbf{c} cdot 153^{circ} ) D. ( 156^{circ} ) | 8 |

236 | 8. Find the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5. | 8 |

237 | ff ( A(-2,1), B(a, 0), C(4, b) ) and ( D(1,2) ) are the vertices of parallelogram ( A B C D, ) find ( a ) and ( b . ) Hence find the length of it’s sides. | 8 |

238 | IV 3. In Fig, bisectors of B and 2D of quadrilateral ABCD meet CD and AB produced at P and respectively. Prove that P+2Q= ZABC + ZADC). BQ W PD | 8 |

239 | ABCD is a trapeziumin which AB is parallel to DC. If the diagonals intersect at ( 0, ) then which one of the following is correct? A ( cdot frac{O A}{O C}=frac{O B}{O D} ) в. ( frac{A D}{B C}=frac{A B}{D C} ) c. ( frac{O B}{O D}=frac{B C}{C D} ) D. ( frac{O A}{O C}=frac{D A}{D C} ) | 8 |

240 | ABCD is a parallelogram, ( A E perp D C ) and ( boldsymbol{C F} perp boldsymbol{A D} . ) If ( boldsymbol{A B}=mathbf{1 6} mathrm{cm}, boldsymbol{A} boldsymbol{E}=mathbf{8} c boldsymbol{m} ) and ( boldsymbol{C F}=mathbf{1 0} mathrm{cm}, ) find ( boldsymbol{A} boldsymbol{D} ) | 8 |

241 | How many sides does a regular polygon have if the measure of an exterior angle is ( 24^{0} ? ) A . 14 B. 13 c. 15 D. 18 | 8 |

242 | Is it possible to have a polygon, whose sum of interior angles is ( 870^{circ} ) Answer: No State true or false: A. True B. False | 8 |

243 | The three vertices of a parallelogram taken in order are (-1,0),(3,1) and (2,2) respectively.Find the coordinates of the fourth vertex | 8 |

244 | The measure of the external angle of a regular octagon is ( mathbf{A} cdot pi / 4 ) в. ( pi / 6 ) c. ( pi / 8 ) D. ( pi / 12 ) | 8 |

245 | If one angle of a parallelogram is ( 65^{circ} ) What are the other angles? A ( .50^{circ}, 120^{circ}, 50^{circ} ) в. ( 115^{circ}, 65^{circ} ), ( 115^{circ} ) ( mathbf{c} cdot 65^{circ}, 115^{circ}, 65^{circ} ) D. None of the above | 8 |

246 | 8. In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x. 300 130° C D | 8 |

247 | The angles of a pentagon are in the ratio ( 4: 8: 6: 4: 5 . ) Find each angle of the pentagon. A ( cdot 40^{circ}, 160^{circ}, 120^{circ}, 80^{circ} )and ( 100^{circ} ) B . ( 60^{circ}, 160^{circ}, 120^{circ}, 80^{circ} ) and ( 100^{circ} ) c. ( 80^{circ}, 160^{circ}, 120^{circ}, 80^{circ} ) and ( 100^{circ} ) D. ( 30^{circ}, 160^{circ}, 120^{circ}, 80^{circ} ) and ( 100^{circ} ) | 8 |

248 | 3. In a quadrilateral ABOD. A nad Barette beds ZA and B respectively. Prove that 2 403 = 1 / 1 / C + LD) | 8 |

249 | ( A B C D ) is a trapezium with parallel ( operatorname{sides} A B=a c m ) and ( D C=b c m . E ) and ( F ) are the mid-points of the non- parallel sides. The ratio of ( a r(A B F E) ) and ( a r(E F C D) ) is ( A cdot a: b ) B. ( (3 a+b):(a+3 b ) ( c cdotleft(a+3 b_{cdot}(3 a+b)right. ) D. ( (2 a+b):(3 a+b) ) | 8 |

250 | ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on AB Prove that (i) ( a r(A B C D)= ) ( a r(A B E F) ) (ii) ( a r(A B C D)=A B times D G ) | 8 |

251 | State true false: It is possible to have a polygon whose sum of interior angles is ( 630^{circ} ) A. True B. False | 8 |

252 | Is it a closed curve? | 8 |

253 | In a parallelogram ABCD if ( A B=2 x+5 ) ( mathrm{CD}=mathrm{y}+1, mathrm{AD}=mathrm{y}+5 ) and ( mathrm{BC}=3 mathrm{x}-4 ) then ratio of ( A B: B C ) is ( A cdot 71: 21 ) B. 12:11 c. 31: 35 D. 4 : 7 | 8 |

254 | PQRS is a parallelogram. If ( L, M ) are the midpoints of ( Q R ) and ( P S ) respectively, and ( O ) is any point on ( L M ) then the area of triangle ( O P Q ) is equal to A ( cdotleft(frac{1}{3}right)^{r d} ) of the parallelogram ( P Q R S ) B ( cdotleft(frac{1}{4}right)^{t h} ) of the parallelogram ( P Q R S ) C ( cdotleft(frac{1}{2}right) ) of the parallelogram ( P Q R S ) D ( left(frac{1}{6}right)^{t h} ) of the parallelogram ( P Q R S ) | 8 |

255 | 9. In the isosceles trapezium PQRS with PQ || RS and QR = PS, which of the following is correct? (a) ZP+ZS=180° and ZQ+ZR=180° (b) PS = QR and PR = QS (c) ZP=2Q and ZR= ZS (d) All of the above | 8 |

256 | 1. To construct a quadrilateral, if 3 angles are given then how many included sides are required. | 8 |

257 | Find the measure of each exterior angle of a regular polygon of 15 sides A ( cdot 24^{circ} ) B. ( 30^{circ} ) ( c cdot 36^{0} ) D. ( 42^{circ} ) | 8 |

258 | 5. Given AB = 3 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following is false about the construction of a quadrilateral? (a) It is possible to draw the quadrilateral. (b) It is not possible to draw the quadrilateral since AD+ DC<AC. (c) It is possible to draw the quadrilateral since AD+DC <AC (d) None of these | 8 |

259 | The slope of a curve at each of its points is equal to the square of the abscissae of the point. Find the particular curve through the point (-1,1) | 8 |

260 | Prove that parallelograms are on the same base and between the same parallel lines are equal in area. | 8 |

261 | An exterior angle of regular polygon is ( 12^{circ} ) the sum of all the interior angles is A ( cdot 4040^{circ} ) B . ( 5040^{circ} ) c. ( 6040^{circ} ) D. ( 7040^{circ} ) | 8 |

262 | 2. To construct a quadrilateral, if 2 diagonals are given, then how many sides are required. | 8 |

263 | A polygon has 44 diagonals. Find the number of its sides. | 8 |

264 | 2. All rectangles are also squares. | 8 |

265 | Let ABCD be a parallelogram. Let AP, CQ be the ( perp ) from ( A ) and ( C ) on its diagonal BD. Which of the following is true. This question has multiple correct options A. ( C Q=P D ) в. ( P D=Q B ) c ( . A P=C Q ) D. ( A P=B Q ) | 8 |

266 | The interior angle of a regular polygon is ( mathbf{1 5 6}^{circ} ). Find the number of sides of the polygon. | 8 |

267 | In the figure, find the measure of ( angle M P N ) | 8 |

268 | The area of the parallelogram ABCD is ( 90 c m^{2}(text { see Fig.9.13 ) EC }=F D . ) Find ( boldsymbol{A}(boldsymbol{A} boldsymbol{B} boldsymbol{E} boldsymbol{F}) ) ( mathbf{A} cdot 45 c m^{2} ) B. ( 60 mathrm{cm}^{2} ) ( mathrm{c} cdot 90 mathrm{cm}^{2} ) D. ( 180 mathrm{cm}^{2} ) | 8 |

269 | 5. In the given parallelogram YOUR, Z RUO= 120° and OYis extended to point S such that Z SRY= 50°. Find YSR U 12000 | 8 |

270 | Find the area ( left(text { in } m^{2}right) ) of the trapezium PQRS with height PQ given in the figure. | 8 |

271 | Measures of opposite angles of parallelogram are ( (3 x-2)^{circ} ) and ( (50- ) ( x)^{circ} . ) Find the measure of its other angles. A . 143 в. 153 ( c cdot 163 ) D. 173 | 8 |

272 | 9. If two adjacent angles of a parallelogram are in the ratio 4:5, then the measure of the angles not equal to is (a) 80°, 100° (b) 160°, 200° (c) 40°,50° (d) 114°, 36° | 8 |

273 | 53. The difference between the exte- rior and interior angles at a ver- tex of a regular polygon is 150°. The number of sides of the poly- gon is (1) 10 (2) 15 (3) 24 (4) 30 | 8 |

274 | The triangle, quadrilateral, pentagon are all examples of A. diagonal B. open curve c. polygon D. circles | 8 |

275 | In a regular polygon, the exterior and interior angles are in the ration 1: 4 The number of sides of the polygon is A . 10 B. 12 c. 15 D. 16 | 8 |

276 | If ( A B C D ) is a parallelogram and ( Q ) and ( R ) are the circumcentres of the triangles ( A B C ) and ( A D C ) respectively, then ( A Q C R ) is always A. A rectangle B. A trapezium c. A rhombus D. None of these | 8 |

277 | measurements can determine a quadrilateral uniquely. | 8 |

278 | 7. IfABCD is a parallelogram, then ZA-ZC=……….. . 100 | 8 |

279 | How many diagonals does a triangle have? ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) ( D ) | 8 |

280 | The number of sides of two regular polygons A and B are in ratio 1: 3. If each interior angle of polygon ( mathrm{B} ) is ( 168^{circ} . ) Find each interior angle of polygon ( A ) A ( .144^{circ} ) B. 120 ( c cdot 72 ) D. 22.5 | 8 |

281 | In a square ( A B C D, angle A B D=3 x= ) ( angle A D B, ) then ( angle B D C ? ) ( mathbf{A} cdot 6 x^{circ} ) B. ( (90-6 x)^{text {d }} ) ( mathbf{c} cdot 45^{circ} ) D. None | 8 |

282 | ( A B C D ) is a rhombus and ( P, Q, R ) and ( S ) are the mid-points of the sides ( A B, B C, C D ) and ( D A ) respectively. Show that the quadrilateral ( P Q R S ) is a rectangle | 8 |

283 | Find the measure of ( angle P, ) if ( overline{S P} | overline{R Q} ) in the given figure. | 8 |

284 | In fig. ABCD is a parallelogram. What are the values of ( p ) and ( q ? ) If ( angle C B E=100^{circ} ) ( mathbf{A} cdot angle p=100^{circ}, angle q=80^{circ} ) B . ( angle p=80^{circ}, angle q=100^{circ} ) c. ( angle p=angle q ) D. None | 8 |

285 | Polygons that have no portions of their diagonals in the exterior are called A. squares B. triangles c. convex D. concave | 8 |

286 | In the figure above (not to scale) ABCD is trapezium in which ( overline{boldsymbol{A B}} | overline{boldsymbol{C D}}, mathbf{A D}= ) ( mathrm{CD} ) and ( mathrm{AB}=2 mathrm{CD} ) If ( angle A D C=100^{circ} ) then find ( angle A B C ) A ( cdot 40^{circ} ) B .50 ( c cdot 60^{circ} ) D. 70 | 8 |

287 | 10. In the figure, find the value of x. a 850 a 3. In m V89° | 8 |

288 | Plane figure with four sides is known as ( mathbf{a} ) A. Pentagon B. Trianglel c. Quadrilateral D. none of these | 8 |

289 | A rectangular paper of length ( 45 mathrm{cm} ) and breadth ( 5 mathrm{cm} ) is cut to form a square with the same area. What is the side of the square? | 8 |

290 | In a trapezium. ABCD, ( angle A D C=110^{circ} ) Find ( angle boldsymbol{A} ) A ( .50^{circ} ) B. ( 60^{circ} ) ( c .70^{circ} ) D. ( 80^{circ} ) | 8 |

291 | Instruments used to draw circle A. scale and setsquare B. scale and protractor C. scale and compass D. scale | 8 |

292 | Prove that line segment joining the mid- points of the diagonals of a trapezium is parallel to the parallel sides and equal to half their difference. | 8 |

293 | The vertices of a convex polygon point are A. outwards B. inwards c. middle D. extreme corner | 8 |

294 | In the above figure both RISK and CLUE are parallelograms. Find the value of ( x ) | 8 |

295 | 1. PUUTTEL 9. Four angles of a quadrilateral are in the ratio 3:5:7:9. Find the angles. Sol. Suppose the measure of four angles are 3x, 5x, 7x and 9r Bangla | 8 |

296 | 7. In the diagram, ABCD is a rhombus. The value of x-yis: (a) 50° (c) 30° | 8 |

297 | ( square_{0} ) 0 ( Delta ) | 8 |

298 | Two regular polygons are such that the ratio between their number of sides is 1: 2 and the ratio of measures of their interior angles is ( 3: 4 . ) Find the number of sides of each polygon. | 8 |

299 | Prove that if the diagonals of a parallelogram are equal then it is a rectangle. | 8 |

300 | ( A B C D ) is a rectangle with ( angle A B D= ) ( 40^{circ} . ) Determine ( angle D B C ) | 8 |

301 | What do you call a parallelogram which has equal diagonals? A. A trapezium B. A rectangle c. A rhombus D. A kite | 8 |

302 | A simple closed curve made up of only line segments is called a A . Curve B. Polygon c. surface D. concave | 8 |

303 | ABCDE…… is part of a polygon which has interior angles of ( 160^{0} . ) CDLM is a Square. Find the value of ( x ) and ( y ) respectively. A. 70,105 B. 70,150 c. 105,70 D. 150,70 | 8 |

304 | What is the length of the other sides of the rectangle as shown in the figure, if side ( A B=10 ) and ( B C=7 ? ) ( A cdot C D=10 ) and ( A D=5 ) B. ( C D=10 ) and ( A D=7 ) ( c cdot C D=7 ) and ( A D=7 ) D. ( C D=7 ) and ( A D=10 ) 0 | 8 |

305 | How many sides does a polygon have whose sum of the interior angles is ( 1980^{circ} ? ) A . 10 B. 13 c. 11 D. None of these | 8 |

306 | If the interior angle of a regular polygon exceeds the exterior angle by ( 132^{circ}, ) then the number of sides of the polygon is : A . 15 B. 14 c. 13 D. 12 | 8 |

307 | In a given square ( A B C D, ) if the area of triangle ( A B D ) is ( 36 mathrm{cm}^{2}, ) find (i) the area of triangle ( B C D ; ) (ii) the area of the square ( A B C D ) | 8 |

308 | In the following figure, ABCD is a parallelogram. Then find the value of ( x ) | 8 |

309 | If the non-parallel sides of a trapezium are equal, then it is cyclic. A. True B. False | 8 |

310 | State true or false: In a trapezium ( A B C D ) in which ( A B ) is parallel to ( D C ) and ( A D=B C ), then ( angle A D C=angle B C D ) A. True B. False | 8 |

311 | In the following figures, ( A B C D ) is a rhombus. Find the values of ( x ) and ( y ) ( mathbf{A} cdot 50^{circ}, 50^{circ} ) B ( cdot 30^{circ}, 50^{circ} ) c. ( 20^{circ}, 50 ) D. None of these | 8 |

312 | Show that the points (2,-2),(8,4),(5,7) and (-1,1) taken in order constitute the vertices of a Rectangle. | 8 |

313 | A parallelogram whose all sides are equal is called A. Square B. Rhombus c. Rectangle D. Trapezium | 8 |

314 | In the given figure, two identical regular hexagons are placed side by side as shown. Find the value z. ( mathbf{A} cdot 60^{circ} ) ( mathbf{B} cdot 90^{circ} ) ( mathbf{C} cdot 120^{circ} ) D. ( 160^{circ} ) | 8 |

315 | Can it be possible that an interior angle of a regular polygon is ( 22^{circ} ? ) A. True B. False c. Ambiguous D. Data Insufficient | 8 |

316 | 040191 The number of measurements required to construct a quadrilateral is IS | 8 |

317 | The angles of a pentagon in degrees are ( boldsymbol{y}^{o},left(boldsymbol{y}+mathbf{2 0}^{o}right),left(boldsymbol{y}+mathbf{4 0}^{o}right),left(boldsymbol{y}+mathbf{6 0}^{o}right) ) and ( left(y+80^{circ}right) . ) The smallest angle of the pentagon is ( A cdot 88^{circ} ) B. ( 78^{circ} ) ( c cdot 68^{circ} ) ( D cdot 58^{circ} ) | 8 |

318 | 3. A square is a rhombus in which A rhomhus has all its sides of | 8 |

319 | in two reg he ratio 5 between of the poly. 53. The number of sides in two ular polygons are in the rati 4 and the difference betw each interior angle of the gons is 6º. Then the number sides are (1) 15, 12 (2) 5, 4 (3) 10,8 (4) 20, 16 | 8 |

320 | The interior angles of a pentagon are in the ratio ( 4: 5: 6: 7: 5 . ) Find each angle of the pentagon A ( cdot 80^{circ}, 100^{circ}, 120^{circ} 140^{circ} ) and ( 100^{circ} ) ( ^{circ} ) В. ( 100^{circ}, 120^{circ}, 110^{circ}, 140^{circ} ) and ( 100^{circ} ) D. none of the above | 8 |

321 | ( A B C D ) is a rectangle and ( P, Q, R ) and ( s ) are mid-points of the side ( A B, B C, C D ) and DA respectively. Show that the quadrilateral PQRS is a rhombus. | 8 |

322 | Which of the following options shows the same property between a rectangle and a square? A. Both have only 1 pair of parallel lines B. Both have all the angles of measure ( 90^{circ} ) c. Diagonals cut each other perpendicularly D. Both have all sides of equal length | 8 |

323 | Match List I with List II and select the correct answer using the codes given below the lists | 8 |

324 | ( A B C D ) is a parallelogram and ( A P ) and ( C Q ) are perpendiculars from vertices ( A ) and ( C ) on diagonal BD( see Fig.). Show that ( mathbf{A P}=mathbf{C Q} ) | 8 |

325 | If ( A B C D ) is a parallelogram with two adjacent angles ( A ) and ( B ) equal to each other, then the parallelogram is? A. Rhombus B. Trapezium c. Rectangle D. None of These | 8 |

326 | The length of one side of a parallelogram is ( 17 mathrm{cm} ). If the length of its diagonals are ( 12 mathrm{cm} 26 mathrm{cm} ), then find the length of the other side of a parallelogram. | 8 |

327 | If each angle of a regular polygon is ( 135^{circ}, ) how many sides does it have? ( A cdot 6 ) B. 7 ( c cdot 8 ) D. 9 | 8 |

328 | ( A B C D ) is a trapezium in which ( A B | D C ) and its diagonals intersect each other at the point ( O . ) Show that ( frac{A O}{B O}=frac{C O}{D O} ) | 8 |

329 | A parallelogram whose sides are ( 10 mathrm{cm} ) and ( 5 mathrm{cm} ) has one diagonal of ( 8 mathrm{cm}, ) then the length of the other diagonal is ( mathbf{A} cdot 12 mathrm{cm} ) B. ( 11 mathrm{cm} ) ( mathrm{c} cdot 14 mathrm{cm} ) D. None of these | 8 |

330 | Find the area of a square whose perimeter is ( 160 mathrm{m} . ) A floor ( 3.0 mathrm{m} ) long and ( 2.0 mathrm{m} ) wide is to be covered with square shaped tiles of length ( 10 mathrm{cm} . ) Find the cost of flooring it, if the cost of tiles is Rs.150 per 100 tiles. | 8 |

331 | The base angles of a issoceles trapezium are A. unequal B. equal c. circular D. diagonals | 8 |

332 | 4. Which of the following is/are concave polygon? (a) B2 (b) F ) В (d) 0 А В 11. 11. . | 8 |

333 | maTCHING WIL W U WUJU U WUND BUILD CUUMIL-11. Column-I Column-II (A) Parallelogram (B) Rhombus (C) Rectangle (p) opposite sides are equal. (9) Diagonals are equal. (r) Diagonals bisect each other. (D) Square (s) opposite angles are equal. (t) All sides are equal. | 8 |

334 | In triangle ( A B C, D ) and ( E ) are mid- points of sides ( A B ) and ( B C ) respectively. Also, ( boldsymbol{F} ) is a point in side ( A C ) so that ( D F ) is parallel to ( B C ) Find the perimeter of parallelogram ( D B E F, ) if ( A B=10 mathrm{cm}, B C=8 cdot 4 mathrm{cm} ) and ( A C=12 mathrm{cm} ) A ( .28 .7 mathrm{cm} ) в. ( 22.5 mathrm{cm} ) c. ( 18.4 mathrm{cm} ) D. ( 18.5 mathrm{cm} ) | 8 |

335 | DA In the above figure, ABCD is a square and BCE is an equilateral triangle, what is the measure of angle DEC? (a) 15° (b) 30° (c) 20° (d) 45° | 8 |

336 | the given figure lines p and q are parallel. Find value of x so that lines land m be parallel. m | 8 |

337 | Find the ZADC, ZECF and ZEBC in the below given figure. | 8 |

338 | Diagonals of a rectangle are: A. equal to each other B. not equal C. one is double of other D. none | 8 |

339 | In the figure given below ( square P Q R S ) is a trapezium. seg ( boldsymbol{P Q}|operatorname{seg} boldsymbol{M} boldsymbol{N}| operatorname{seg} boldsymbol{S} boldsymbol{R} ) If ( boldsymbol{P} boldsymbol{M}=mathbf{8}, boldsymbol{M} boldsymbol{S}=mathbf{1 0} ) and ( boldsymbol{N} boldsymbol{R}=mathbf{5} ) then find ( Q N ) | 8 |

340 | Two consecutive sides of a parallellogram are ( 4 x+5 y=0 & 7 x+ ) ( 2 y=0 . ) If the equation to one diagonal is ( 11 x+7 y=9, ) find the equation to the other diagonal. | 8 |

341 | – How many sides does a regular polygon have if each of its interior angles is 1657 | 8 |

342 | Given ABCD is a parallelogram, find the measure of ( x-2 y+z ) in degrees form the following figure | 8 |

343 | State whether True or False. (a) All rectangles are squares. (b) All rhombuses are parallelograms. (c) All squares are rhombuses and also rectangles. (d) All squares are not parallelograms. (e) All kites are rhombuses. (f) All rhombuses are kites. (g) All parallelograms are trapeziums. (h) All squares are trapeziums. | 8 |

344 | Side of a square is ( 5 mathrm{cm} ). What is the length of its diagonal. | 8 |

345 | How many sides does a regular polygon have if each of its interior angles is ( mathbf{1 6} mathbf{5}^{mathbf{0}} ) ? A. Number of sides ( =24 ) B. Number of sides= 30 c. Number of sides ( =36 ) D. Number of sides ( =42 ) | 8 |

346 | ABCD is a parallelogram in which ZDAB=75º and ZDBC = 60° then ZCDB= | 8 |

347 | Find ( angle C ) in the figure if ( overline{A B} | overline{D C} ) | 8 |

348 | 7. Which quadrilateral have four sides of equal length? (a) Rhombus (b) Rectangle (c) Parallelogram (d) Square | 8 |

349 | Show that the four triangles as shown in the adjoining fig. formed by diagonals and sides of rhombus are congruent. | 8 |

350 | The sides of a quadrilateral are produced in order. What the sum of the four exterior angles? | 8 |

351 | 4. Look at the angles in this quadrilateral. Which angle measure is closest to 48°? | 8 |

352 | 1. All regular polygons are | 8 |

353 | Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that) What can you say about the angle sum | 8 |

354 | A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identity the regular quadrilateral? | 8 |

355 | Perimeter of rectangle is- – A ( .2(l times b) ) в. ( 2(l+b) ) c. ( (l times b times h) ) D. None of these | 8 |

356 | In a parallelogram ( A B C D, A B=10 mathrm{cm} ) and ( A D=6 mathrm{cm} . ) The bisector of ( A ) meets DC in E. AE and BC produced meet at F. Find the length of CF. ( A cdot 3 mathrm{cm} ) B. ( 4 mathrm{cm} ) ( c cdot 5 mathrm{cm} ) ( D cdot 6 mathrm{cm} ) | 8 |

357 | Find the measure of each angle of a parallelogram, one its angle is 30 less than twice the smaller angle. | 8 |

358 | Fed the measure of each angle of a parallelogram, if one of ** angles is 30° less than twice the smallest angle. S P2-30° 2x-30° | 8 |

359 | Explain how a square is a rectangle. Answer: A square is a parallelogram with each angle a right angle; so it is a rectangle. A. True B. False | 8 |

360 | 3. Which of the following statement(s) is/are true? (a) A parallelogram in which two adjacent angles are equal is a rectangle. (b) A quadrilateral in which both pairs of opposite angles are equal is parallelogram. (c) In a parallelogram, the number of acute angles is zero or two. (d) None of these | 8 |

361 | 2. In the figure given below AN and CP are perpendiculars to the diagonal BD of a parallelogram. Then (a) AN=CP (c) ANCP (d) None of these | 8 |

362 | PQRS is a parallelogram and ( angle 1 ) and ( angle 2 ) are two exterior,angles, then ( angle 1= ) ( angle 2=angle 3=angle 4 ) A. True B. False | 8 |

363 | If ( A B C D ) is a parallelogram, ( A E perp ) DC and ( boldsymbol{C F} perp boldsymbol{A D} ). If ( boldsymbol{A B}=mathbf{1 6 c m} ) ( A E=8 c m ) and ( C F=10 mathrm{cm}, ) find ( A D ) | 8 |

364 | In the pentagon ( A B C D E ) shown above, the measures of angles ( A, E ) and ( C ) are given. It is known that the measures of angles ( B ) and ( D ) are equal.Then which of the following is true? ( mathbf{A} cdot overline{A B} | overline{C D} ) ( mathbf{B} cdot overline{B C} | overline{A E} ) ( mathbf{c} cdot overline{A B} | overline{D E} ) D. ( overline{C D} | overline{A E} ) | 8 |

365 | Show that the diagonals of a parallelogram divide it into four triangles of equal area. | 8 |

366 | Position of Q is A. Interior of curve B. Exterior of curve c. on the curve can not be said | 8 |

367 | 4. The diagonals of a rectangle ABCD meet at O. If ZBOC 44″, find ZOAD | 8 |

368 | Give reasons for the following. Squares, rectangles, parallelograms are all quadrilaterals. | 8 |

369 | The ratio of the measure of the angles in a rhombus is ( 2: 7 . ) What is the measure of the four angles? В. ( 40^{circ}, 140^{circ}, 40^{circ}, 140^{circ} ) C ( cdot 65^{circ}, 115^{circ}, 65^{circ}, 115^{circ} ) D. None of the above | 8 |

370 | 3. Find the angle measurex in the following figures. 50 130° 1200 609 (iv) | 8 |

371 | 15. The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45º. Find the angles of the parallelogram. | 8 |

372 | Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that) What can you say about the angle sum | 8 |

373 | A square of side ( a ) lies above the ( x ) -axis and has one vertex at the origin. The side passing through it makes an angle ( left(0<alpha<frac{pi}{4}right) ) with the positive direction of ( x ) -axis. The equation of its diagonal not through the origin A ( cdot y(cos alpha-sin alpha)-x(sin alpha-cos alpha)=a ) B cdot ( y(cos alpha+sin alpha)+x(sin alpha-cos alpha)=a ) c. ( y(cos alpha+sin alpha)+x(sin alpha+cos alpha)=a ) D・ ( y(cos alpha+sin alpha)+x(cos alpha-sin alpha)=a ) | 8 |

374 | The perimeter of a rhombus is ( 100 mathrm{cm} ) and one of the diagonals is ( 40 mathrm{cm} ) Then the area of the rhombus is A. ( 1000 mathrm{cm}^{2} ) В. ( 500 mathrm{cm}^{2} ) c. ( 1200 mathrm{cm}^{2} ) D. ( 600 mathrm{cm}^{2} ) | 8 |

375 | ( A B C D ) is a quadrilateral in which ( A B ) and ( C D ) are smallest and longest sides respectively. Prove that ( angle A>angle C a n d angle B>angle D ) | 8 |

376 | ( A B C D ) is a quadrilateral in which ( P, Q, R ) and ( S ) are mid-points of the ( operatorname{sides} A B, B C, C D ) and ( D A ) respectively. Show that ( P Q R S ) is a parallelogram. | 8 |

377 | 5. The angles of a quadrilateral are in the ratio 1:3:4:7. Find all the angles of the quadrilateral. | 8 |

378 | Identify the number of polygons from the given figures? A . 5 B . 2 ( c cdot 6 ) D. 3 | 8 |

379 | 13. Name the quadrilaterals whose diagonals. (i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal. C | 8 |

380 | Three of the exterior angles of a hexagon are ( 40^{circ}, 51^{circ} ) and ( 86^{circ} . ) If each of the remaining exterior angles is ( x^{circ}, ) find the value of ( x ) A . 58 B. 61 c. 65 D. none of the above | 8 |

381 | A polygon with minimum number of sides is called as ? A. pentagon B. square c. triangle D. angle | 8 |

382 | Diagonals ( A C ) and ( B D ) of a trapezium ( A B C D ) with ( A B | D C ) intersect each other at ( O . ) Prove that ( a r(A O D)= ) ( boldsymbol{a} boldsymbol{r}(boldsymbol{B O C}) ) | 8 |

383 | PQRS is a isosceles trapezium with ( boldsymbol{P Q} | boldsymbol{R S}, ) if ( mathrm{P}=mathbf{6 0}, ) then ( mathrm{Q} ) equals to A . 120 B . 30 ( c .60 ) D. 150 | 8 |

384 | The parallel sides of the trapezium are known as (a) bases (b) perpendiculars (c) hypotenuse (d) none | 8 |

385 | A metal box with a square base and vertical height is to contain ( 1024 mathrm{cm}^{2} ) The material for the top and the bottom ( operatorname{costs} mathrm{Rs} .5 / mathrm{cm}^{2} ) and the material for the sides costs Rs. ( 2.50 / c m^{2} ). Find the least ( operatorname{cost} ) of the box. | 8 |

386 | A rectangular MORE is shown below: M Answer the following questions by giving appropriate reason. ( IS RENOM? (ii) Is ZMYO= ZRXE? (1) Is ZMOY= Z REX? (iv) Is AMYO= ARXE? (v) IS MY =RX? | 8 |

387 | ( A B C D ) is a trapezium in which ( A B|| C D ) and ( A D=B C . ) Show that ( angle A=angle B ) | 8 |

388 | If ( D, E, F ) are the mid-points of the sides ( B C, C A ) and ( A B ) respectively of ( triangle A B C, ) prove that ( B D E F ) is a parallelogram whose area is half to that of ( triangle A B C . ) Show that ( a r(triangle D E F)= ) ( frac{1}{4} a r(triangle A B C) ) | 8 |

389 | How many diagonals does a regular hexagon have? ( mathbf{A} cdot mathbf{8} ) B. 9 c. 10 D. 1 | 8 |

390 | State true or false: In a square ( A B C D ), diagonals meet at O. ( P ) is a point on ( B C ) such that ( O B= ) ( B P, ) then ( angle P O C=left(22 frac{1}{2}right)^{0} ) A. True B. False | 8 |

391 | Find the number of sides of a regular polygon if each exterior angle measures: ( 45^{circ} ) | 8 |

392 | & in the diagram. ABCD is a rhombus. AFC and BED are straight lines p+q+r+s+t=? (a) 2000 (c) 360° (b) 270° (d) 540°C | 8 |

393 | Let ( A B C D E F ) be a convex hexagon in which the diagonals ( A D, B E, C F ) are concurrent at ( O . ) Suppose the area of triangle ( O A F ) is the geometric mean of those of ( O A B ) and ( O E F ; ) and the area of triangle ( O B C ) is the geometric mean of those of ( boldsymbol{O} boldsymbol{A} boldsymbol{B} ) and ( boldsymbol{O} boldsymbol{C} boldsymbol{D} ). Prove that the area of triangle ( O E D ) is the geometric mean of those of ( O C D ) and OEF. | 8 |

394 | The following figures GUNS and RUNS are parallelograms. Find ( x ) and ( y ) (Lengths are in ( mathrm{cm} ) ) | 8 |

395 | In the parallelogram ABCD the angles ( A ) and ( C ) are obtuse Points ( X ) and ( Y ) are taken on the diagonal BD such that the angles ( mathrm{XAD} ) and ( mathrm{YCB} ) are right angles. And hence, ( boldsymbol{X} boldsymbol{A}=boldsymbol{Y} boldsymbol{C} ) If the above statement is true then mention answer as 1 , else mention 0 if false | 8 |

396 | Is it possible to have a polygon whose sum of interior angles is ( 320^{circ} ? ) A. Yes B. No c. Ambiguous D. Data not sufficient | 8 |

397 | In an isosceles trapezium, the length of the parallel sides, and the lengths of the non-parallel sides are all equal to ( 30 . ) In order to maximize the area of the trapezium, the smallest angle should be ( A cdot frac{pi}{6} ) B. ( c cdot frac{pi}{3} ) D. | 8 |

398 | ms. 7. parallel What is the sum of exterior angles in a convex polygon? | 8 |

399 | There is a regular polygon whose each interior angle is ( 150^{circ} ) State true or false. A. True B. False | 8 |

400 | Find the measure of interior angle. Also name the polygon. | 8 |

401 | A parallelogram has sides ( 6 mathrm{cm} ) and ( 4 mathrm{cm} ) and one of its diagonals is ( 8 mathrm{cm} ) then its area is :- | 8 |

402 | 10. The diagonal of rectangle is thrice its smaller side. The ratio of its sides is | 8 |

403 | 8. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram. UUDIS corallelograms | 8 |

404 | on pnh DIO SIRuspinn TAMA TAna 10. Opposite sides of a trapezium are parallel. | 8 |

405 | A square is rectangle. Give reason | 8 |

406 | Find the perimeter of a rectangular hall, if its length exceeds its breadth by ( 7 mathrm{m} ) and the area of the hall is ( 228 m^{2} ) A. 72 m в. ( 70 mathrm{m} ) ( c .64 mathrm{m} ) D. ( 62 mathrm{m} ) | 8 |

407 | If ( A B C D ) is a rhombus such that ( angle A C B=40^{circ}, ) then ( angle A D B ) is A ( cdot 40^{circ} ) B . ( 45^{circ} ) ( c .50^{circ} ) D. ( 60^{circ} ) | 8 |

408 | Identify closed curve. ( mathbf{A} cdot 1 ) only B. 2 only C. 3 only D. 1 and 2 only | 8 |

409 | In the given figure, ABCD is a parallelogram in which ( angle D A B=75^{circ} ) and ( angle mathrm{DBC}=60^{circ} ) then the measure of ( angle ) BDC is equal to? ( A cdot 75^{circ} ) B. ( 60^{circ} ) ( c cdot 45^{circ} ) D. 55 | 8 |

410 | If ( P ) and ( Q ) are points of trisection of the diagonal BD of a parallelogram ABCD, ( boldsymbol{C Q} | boldsymbol{A P} ) A. True B. False | 8 |

411 | Name the polygon. Make two more examples of same type. | 8 |

412 | One angle of a seven-sided polygon is ( 114^{circ} ) and each of the other six angles is ( x^{circ} . ) The value of ( x ) is? A ( cdot 114^{circ} ) B. 121 ( c cdot 131^{circ} ) D. ( 151^{circ} ) | 8 |

413 | The angles of a pentagon in degrees are ( x, x+20, x+40, x+60 ) and ( x+80, ) then the smallest angle of the pentagon is ( mathbf{A} cdot 50^{circ} ) B. ( 68^{circ} ) ( c cdot 78^{circ} ) D. ( 85^{circ} ) | 8 |

414 | Illustrate, if possible the following with a rough diagram: A closed curve that is not a polygon. | 8 |

415 | In the above figure both RISK and CLUE are parallelograms. Find the value of ( x ) | 8 |

416 | State true or false: The diagonal ( B D ) of a parallelogram ( A B C D ) bisects angles ( B ) and ( D ). then ( A B C D ) is a rhombus. A. True B. False | 8 |

417 | In the quadrilateral ( A B C D ), the diagonals ( A C ) and ( B D ) are equal and perpendicular to each other. What type of a quadrilateral is ( A B C D ? ) A. A square B. A parallelogram c. A rectangle D. A trapezium | 8 |

418 | The area of a rhombus is ( 28 m^{2} . ) If its perimeter is ( 28 mathrm{m} ), find its altitude. | 8 |

419 | 4. In parallelogram PQRS, O is the mid point of SQ. Find ZS ZR, PQ, QR and diagonal PR. s 15cm R 11cm 6 cm 1600 AZ | 8 |

420 | The sum of the measures of interior angles of a polygon of ( n ) sides is equal to A. ( 2 n ) right angles B. ( (2 n-2) ) right angles c. ( 2(n-2) ) right angles D. ( 2(n-4) ) right angles | 8 |

421 | ( A B C D ) is a trapezium in which ( A B ) is parallel to ( D C ). If the diagonals intersect at ( O ), then which one of the following is correct? A ( cdot frac{O A}{O C}=frac{O B}{O D} ) в. ( frac{A D}{B C}=frac{A B}{D C} ) c. ( frac{O B}{O C}=frac{B C}{C D} ) D. ( frac{O A}{D C}=frac{D A}{D C} ) | 8 |

422 | ( P ) and ( Q ) are any two points lying on the sides ( D C ) and ( A D ) respectively of a parallelogram ( A B C D . ) Show that ( boldsymbol{a r}(boldsymbol{A P B})=boldsymbol{a r}(boldsymbol{B Q C}) ) | 8 |

423 | ( A B C D ) is a square, ( X ) and ( Y ) are points on sides ( A D ) and ( B C ) respectively, such that ( A Y=B X . ) Prove that. ( angle B A Y=angle A B Y ) | 8 |

424 | In a rhombus PQRS, PR = 24 cm and QS ( =18 mathrm{cm} . ) Find the perimeter of the rhombus. | 8 |

425 | 5. Find the measure of each exterior angle of a regular polygon of ( 9 sides (11) 15 sides | 8 |

426 | 3. three line segments. In which condition a polygon is called a regular polygon? The sides of quadrilateral arenroduced in order What is | 8 |

427 | 59. Each internal angle of regu- lar polygon is two times its external angle. Then the num- ber of sides of the polygon is : (1) 8 (2) 6 (3) 5 (4) 7 | 8 |

428 | In Fig, ABCD is a parallelogram in which ĐDAB = 75°. ĐDBC = 60° then the value ofĐCDB and ĐADB is 12k. Find the value of k. 750 | 8 |

429 | 110 ausunu If the diagonals of a parallelogram bisect each other at right angles, then it is a | 8 |

430 | The measure of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallellogram. tonalen of parallelogram have equal measure | 8 |

431 | ( A B C D ) is a rectangle such that ( A C+ ) ( A B=5 A D ) and ( A C-A D=8, ) then the area of rectangle ( A B C D ) is A . 36sq. units B. 50. sq. units c. 60 sq. units D. cannot be found | 8 |

432 | The number of sides of two regular polygons ( A ) and ( B ) are in the ratio 1: 3.1 each interior angle of polygon ( mathrm{B} ) is ( 168^{circ} ) find each interior angle of polygon ( boldsymbol{A} ) A ( .144^{circ} ) B. 124 ( c cdot 134^{circ} ) D. none of the above | 8 |

433 | 2. Assertion : A polygon having 16 sides is called 16 sider polygon or 16-gon. Reason: A polygon bounded by n-line segments is called n-sides polygon or n-gon. A contin u emile. -1 | 8 |

434 | Given are some figures. Classify each of these figures on the basis of the following: (i) simple curve (ii) simple closed curve (iii) polygon (iv) Convex polygon (iv) convex polygon (v) concave polygon (vi) Not a curve | 8 |

435 | a The measure of Z A and Bis (a) 1159.650 (b) 100°, 180° (c) 950.850 (d) 750, 1059 | 8 |

436 | ( A B C D ) is a parallelogram and ( P ) is a point on the segment ( overline{A D} ) dividing it internally in the ratio 3: 1 the line ( overline{B P} ) meets the diagonal ( overline{A C} ) in ( Q . ) Then the ratio ( boldsymbol{A} boldsymbol{Q}: boldsymbol{Q} boldsymbol{C} ) is A .3: 4 B. 4: 3 c. 3: 2 D. 2 : 3 | 8 |

437 | If ( A M ) and ( C N ) are perpendiculars on the disgonal ( B D ) of a parallelogram ( A B C D, ) Is ( triangle A M D cong triangle C N B ? ) Give reason | 8 |

438 | Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1: 5 | 8 |

439 | 2. A parallelogram which has equal diagonals is a (a) Square (b) Rectangle (c) Rhombus (d) None | 8 |

440 | A quadrilateral in which both pairs of opposite sides are parallel is a A . square B. rhombus c. rectangle D. parallelogram | 8 |

441 | Let ABCD be a parallelogram. The diagonals bisect in E. (i) If ( A B=6 mathrm{cm} ) and ( A D=4 mathrm{cm}, ) find ( C D ) and BC. (ii) If ( mathrm{DE}=5 mathrm{cm} ) and ( mathrm{AE}=7 mathrm{cm}, ) find ( mathrm{BD} ) and AC. (iii) If ( angle D A B=72^{circ}, ) find the measure of ( angle C B A ) ( (text { iv ) If } boldsymbol{A} boldsymbol{D}=(boldsymbol{x}+boldsymbol{2} boldsymbol{y}), boldsymbol{B} boldsymbol{C}=(boldsymbol{2} boldsymbol{x}+ ) ( mathbf{3}), boldsymbol{D} boldsymbol{C}=(boldsymbol{x}+boldsymbol{7}) ) and ( boldsymbol{A} boldsymbol{B}=(boldsymbol{3} boldsymbol{y}+boldsymbol{2}) ) find ( A B ) and ( B C ). | 8 |

442 | In the given five sided closed figure, find ( angle boldsymbol{E} boldsymbol{A} boldsymbol{B}+angle boldsymbol{A} boldsymbol{B} boldsymbol{C}+angle boldsymbol{B} boldsymbol{C} boldsymbol{D}+ ) ( angle C D E+angle D E A ) ( 4 cdot 520 ) B. ( 540^{circ} ) ( c .530 ) D. 140 | 8 |

443 | 67. The ratio between the number of sides of two polygon is 2:1 and the ratio between their interior angle is 4 : 3. The number of sides of these polygons are re- spectively: (1) 8,4 (2) 10,5 (3) 12,6 (4) 14,7 | 8 |

444 | The four angles of a quadrilateral are equal. Draw this quadrilateral in your notebook. Find each of them. | 8 |

445 | In a parallelogram ( mathrm{ABCD}, angle B=(2 x+ ) 25)( ^{0} ) and ( angle D=(3 x-5)^{0} . ) Find: (i) The value of ( x ) (ii) Measure of angle. B. ( x=32, b=91 ) degrees, de ( =89 ) degrees c. ( x=30, b=89 ) degrees, d=91 degrees D. ( x=32, b=89 ) degrees, d=91 degrees | 8 |

446 | ABCD is a quadrilateral. If ( A C ) and ( B D ) bisect each other then ABCD must be a A. triangle B. cylinder c. parallelogram D. pyramid | 8 |

447 | ( A B C D ) is a quadrilateral in which all four sides are equal. Show that both pairs of opposite sides are parallel. | 8 |

448 | A polygon which has no diagonal. A. Quadrilateral B. Heptagon c. Triangle D. Pentagon | 8 |

449 | 3. IfBC = 5 cm, then AD= (a) 5cm c) 6 cm (b) 4.8 cm (d) none of these | 8 |

450 | Classify the following curve as open or closed | 8 |

451 | If ( A B C D ) is a parallelogram and ( E, F ) are the centroids of ( triangle A B D ) and ( B C D ) respectively, then ( boldsymbol{E} boldsymbol{F} ) equals ( mathbf{A} cdot A E ) в. ( B E ) c. ( C E ) D. ( D E ) | 8 |

452 | 2. Match the column: Column-I Column-II (A) ABCDE is a regular pentagon. (p) 70° The bisector of Z A of the pentagon meets the side CD in M. Then Z AMC is (B) The angles of a quadrilateral are (q) 80° respectively equal to 1109,50° and 40°. The fourth angle is. (C) In a quadrilateral ABCD, the bisector (r) 90° of Z A and B meet at point P. If ZC=100°, ZD=60°, the mZ APB is (D) Three angles of a quadrilateral are (s) 160° equal: Fourth angle is of measure 150°. The measure of equal angles is | 8 |

453 | The figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides ( 8 mathrm{cm} ) and ( 6 mathrm{cm} ) is A . a rectangle of area ( 24 mathrm{cm}^{2} ) B. a square of area ( 25 mathrm{cm}^{2} ) c. a rhombus of area ( 24 mathrm{cm}^{2} ) D. a trapezium of area ( 12 mathrm{cm}^{2} ) | 8 |

454 | f PQRS is a square, ( A B | S Q ) and ( A C=C B, ) which one is true? A ( . S A=B Q ) B. PC is the bisector of ( angle S P Q ) c. PC if produced will pass through D. All of these | 8 |

455 | Each interior angle of regular polygon is 144º. Find the interior angle of a regular polygon which has double the number of sides as the first polygon. 11 lorom if one of | 8 |

456 | Find the number of sides of a regular polygon whose each exterior angle has a measure of: ( 45^{circ} ) | 8 |

457 | ( boldsymbol{A}(mathbf{5}, mathbf{7}), boldsymbol{B}(mathbf{4}, mathbf{1 2}), boldsymbol{C}(mathbf{9}, mathbf{1 1}) ) and ( boldsymbol{D}(mathbf{1 0}, mathbf{6} ) are four points. Show that ( A B C D ) is a rhombus | 8 |

458 | 3. In rectangle READ, find ZEAR, ZRAD and Z ROD | 8 |

459 | 1. Assertion : A quadrilateral can be constructed if at least any five independent elements are given. Reason : Data about the five parts of a quadrilateral in order to be sufficient must also satisfy (i) the triangle inequality and (ii) angle sum property of a triangle, wherever applicable. | 8 |

460 | 2. Given hore are some figures (Ν) ΣΟΟΡΙΑ (vi) Classify each of them on the basis of the following. (a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon wing figures. | 8 |

461 | The side of a rhombus in ( 5 mathrm{cm} ). If the length of one diagonal of the rhombus is ( 8 mathrm{cm}, ) then find the length of the other diagonal. | 8 |

462 | If the sum of all the angles of a polygon except one angle is ( 2220^{circ}, ) then the number of sides of the polygon is A . 12 B. 13 ( c cdot 14 ) D. 15 | 8 |

463 | If ( boldsymbol{A}(-2,1), B(a, b), C(4,6) ) and ( D(1,2) ) are the vertices of parallelogram. Find ( a+b ) | 8 |

464 | The measurement of each angle of a polygon is ( 160^{circ} . ) The number of its sides is? A . 15 B. 18 c. 20 D. 30 | 8 |

465 | Four angles of a polygon are ( 120^{circ} ) each and the remaining angles are all equal to ( 160^{circ} ) each. Find the number of sides | 8 |

466 | UUUUUUUULI 5. The diagonals of a rhombus bisect | 8 |

467 | ABCDE is regular pentagon. The bisector of ( angle A ) of the pentagon meets the side CD in M. Then the measure ( angle A M C ) is A ( .54^{circ} ) B . ( 45^{circ} ) ( c cdot 90^{0} ) D. ( 100^{circ} ) | 8 |

468 | The bisectors of angles of a parallelogram makes a figure which is A. rectangle B. circle c. pentagon D. octagon | 8 |

469 | Assertion : In a parallelogram if one angle is a right angle, then it is called a rectangle. Reason: In a rectangle if all the sides are equal then it is called a square. | 8 |

470 | If ( A B C D ) is a parallelogram whose diagonals intersect at ( O ) and ( triangle B C D ) is an equilateral triangle having each side of length ( 6 mathrm{cm} ), then the length of diagonal ( boldsymbol{A C} ) is A ( cdot 2 sqrt{3} mathrm{cm} ) B. ( 6 sqrt{3} mathrm{cm} ) c. ( 3 sqrt{6} mathrm{cm} ) D. ( 12 mathrm{cm} ) | 8 |

471 | Draw rough diagrams to illustrate the following: (a) Open curve (b) Closed curve | 8 |

472 | In a trapezium pqrs with ( boldsymbol{P Q} | boldsymbol{S} boldsymbol{R} ) the diagonals ( P R ) and ( Q S ) intersect at ( x ) if ( P Q=frac{2}{3} R S . ) Find the ratio of areas of triangles ( P R Q ) and ( R X S ) | 8 |

473 | Two sticks each of length 7 cm are crossing each other such that they bisect each other at right angles. What shape is formed by joining their end points? Give reason. | 8 |

474 | Find the sum of interior angles of a polygon with 8 sides. | 8 |

475 | ( A B C D ) is a trapezium with ( A B / / D C ) A line parallel to ( A C ) intersects ( A B ) at point ( M ) and ( B C ) at point ( N . ) Prove that area of ( triangle A D M= ) area of ( triangle ) ( A C N ) | 8 |

476 | Show that (-3,2),(-5,-5),(2,-3) and (4,4) are the vertices of a rhombus. | 8 |

477 | Prove that in a parallelogram the opposite angles are equal. | 8 |

478 | 6. Can a quadrilateral ABCD be a parallelogram if () ZD+ ZB=180°? () AB=DC=8 cm, AD=4 cm and BC=4.4 cm? (iii) ZA= 70° and ZC=65°? | 8 |

479 | 4. Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°. | 8 |

480 | 6. Understanding Quadrilaterals 9. In a quadrilateral PQRS; P= 70°, 20=90°; ZR=55° Find the measure of ZS. What kind of quadrilateral is it? Convex or concave. 1 | 8 |

481 | ABCD is a parallelogram in which ZDAO = 40 BAO = 35º and ZCOD = 65°. Find ZODC. 650 R350 | 8 |

482 | In the figure, diagonals ( A C ) and ( B D ) of quadrilateral ( A B C D ) intersect at ( O ) such that ( O B=O D ), show that ( a r(Delta D O C)=a r(Delta A O B) ) | 8 |

483 | A chord is ( 8 mathrm{cm} ) away from the centre of a circle of radius ( 17 mathrm{cm} . ) Find the length of the chord. | 8 |

484 | The diagonal of a rectangle whose length is ( 20 mathrm{cm} ) and breadth in ( 15 mathrm{cm} ) is ( mathbf{A} cdot 35 mathrm{cm} ) B. ( 30 mathrm{cm} ) c. ( 25 mathrm{cm} ) D. ( 40 mathrm{cm} ) | 8 |

485 | What is the name of the quadrilateral which can be drawn from the given data? (a) square (b) Rhombus (c) Parallelogram (d) Rectangle | 8 |

486 | In which quadrilateral all sides and angles are equal? A. rectangle B. parallelogram c. square D. kite | 8 |

487 | A rhombus is symmetrical across – A. its diagonals B. its vertices ( mathrm{C} ). its sides D. its angles | 8 |

488 | In a trapezium ( A B C D ) with ( A B | C D ), it is given that ( A D ) is not parallel to ( B C ). Is ( triangle A B C cong triangle A D C ? ) Given reasons | 8 |

489 | State and draw the lines of symmetry for a rhombus. | 8 |

490 | Give Reason: A square can be thought of as a special rhombus. | 8 |

491 | 3. Assertion : In a regular polygon, i all sides are equal (ii) all interior angles are equal (i) all exterior angles are equal. Reason: A polygon is called regular polygon if all its sida as well as angles are equal. | 8 |

492 | 1. Write the angle-sum property of a quadrilateral. ome of the polygon which is bounded | 8 |

493 | 71. If the sum of interior angles of a regular polygon is equal to two times the sum of exterior angles of that polygon, then the num- ber of sides of that polygon is (1) 5 (2) 6 (3) 7 (4) 8 | 8 |

494 | Classify the following curve as open or closed | 8 |

495 | ( A B C D ) is a rectangular and ( P, Q, R ) and ( S ) are mid points of the sides ( A B, B C, C D ) and ( D A ) respectively. Show that the quadrilateral ( P Q R S ) is a rhombus. | 8 |

496 | Identify open curve. ( mathbf{A} cdot 1 ) only B. 2 only ( mathrm{C} cdot 1,2 ) only D. 3only | 8 |

497 | Formula for polygon is ( (boldsymbol{n}-mathbf{2}) times mathbf{1 8 0}^{boldsymbol{o}} ) A. sum of exterior angles B. sum of interior angles c. number of edges D. number of diagonals | 8 |

498 | In the adjacent rectangle ( A B C D, angle O C D=30^{circ} . ) Calculate ( angle B O C . ) What type of triangle is ( B O C ? ) | 8 |

499 | Name the polygon. Make two more examples of same type. | 8 |

500 | ( A B C D ) is a rectangle in which diagonal ( A C ) bisects ( angle A ) as well as ( angle C . ) Show that: (i) ( A B C D ) is a square (ii) diagonal ( B D ) bisects ( angle B ) as well as ( angle D ) | 8 |

501 | ABCD is a parallelogram as shown in figure. If ( A B=2 A D ) and ( P ) is mid-point of ( A B, ) then ( angle C P D ) is equal to ( A cdot 90^{circ} ) B. ( 60^{circ} ) ( c cdot 45^{circ} ) D. ( 135^{circ} ) | 8 |

502 | 14. ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you) | 8 |

503 | The angle of a pentagon are in the ratio ( 4: 8: 6: 4: 5 . ) Find the greatest angle of the pentagon. ( mathbf{A} cdot 120^{circ} ) B. ( 140^{circ} ) ( c cdot 160^{circ} ) D. 150 | 8 |

504 | Find the number of sides of regular polygon whose measure of each of its interior angle is ( frac{360^{circ}}{7} ) ( A cdot 7 ) B. 8 c. 9 D. 6 | 8 |

505 | ( ln ) a hexagon ( A B C D E F ; ) side ( A B ) is parallel to side ( boldsymbol{F} boldsymbol{E} ) and ( angle boldsymbol{B}: angle boldsymbol{C}: angle boldsymbol{D} ) ( angle E=6: 4: 2: 3 ) Find the measure of ( angle B ) ( mathbf{A} cdot 108 ) B . ( 216^{circ} ) ( c cdot 244^{circ} ) D. None of these | 8 |

506 | State the name of a regular polygon of 4 sides. A. Square B. Trapezium c. Rectangle D. Parallelogram | 8 |

507 | What is the name given to a parallelogram whose all sides are equal ( ? ) | 8 |

508 | Find the number of sides of a regular polygon if each exterior angle is equal to its adjacent interior angle | 8 |

509 | See the figure above Find its perimeter. | 8 |

510 | Two regular polygons are such that the ratio between their number of sides is 1: 2 and the ratio of measure of their interior angles is ( 3: 4 . ) The number of sides of each polygon is A . 5,10 B. 6, 12 c. 4,8 D. 2,3 | 8 |

511 | Find the length of a chord which is at a distance of ( 15 mathrm{cm} ) from the centre of a circle of radius ( 25 mathrm{cm} ) | 8 |

512 | 1. The diagonals of a rectangle ABCD intersect in O. If ZBOC=68°, find Z ODA. D 68° : 121 f ZBAN | 8 |

513 | Number of measurements required to construct a square are A. B. 2 ( c cdot 3 ) ( D ) | 8 |

514 | Let ( A_{0}, A_{1}, A_{2}, A_{3}, A_{4}, A_{5} ) be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments ( A_{0} A_{1}, A_{0} A_{2} ) and ( boldsymbol{A}_{0} boldsymbol{A}_{4} ) is: A ( cdot frac{3}{4} ) B. ( 3 sqrt{3} ) ( c cdot 3 ) D. ( frac{3 sqrt{3}}{2} ) | 8 |

515 | If the sum of all interior angles of a polygon is ( 3240^{circ}, ) how many sides has the polygon? | 8 |

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