CBSE Class 9 Mathematics Quadrilaterals Assignment Set A

Answer 1: A

Answer 2: C

Answer 3: D

Answer 4: C

Answer 5: A

Answer 6: B

Answer 7: A

Answer 8: B

9 ABCD is a quadrilateral. If AC and BD bisect each other, what is ABCD?
(A) A square
(B) A rectangle
(C) A parallelogram
(D) A rhombus
Answer : C

10 In a parallelogram ABCD, ∠D = 60°. Find the measure of ∠A.
(A) 120°
(B) 65°
(C) 90°
(D) 75°
Answer : A

11 ABCD and MNOP are quadrilat erals as shown in the figure.

Which of these is correct?
(A) p + q + r + S = w + x + y + Z
(B) p + q + r + s < w + x + y + z
(C) p + q + r + s > w + x + y + z
(D) p + q + X + y = r + s + w + Z
Answer : A

12 In parallelogram ABCD, AB = 12 cm. The altitudes corresponding to the sides AB and AD are respectively 9 cm and 11 cm.
Find AD.

(A) 108/11 cm
(B) 108/10 cm
(C) 99/10 cm
(D) 108/17 cm
Answer : A

13 In quadrilateral ABCD, if the diagonals AC and BD are equal and perpendicular to each other, what is ABCD?
(A) A square
(B) A parallelogram
(C) A rhombus
(D) A trapezium
Answer : A

14 One of the diagonals of a rhombus is equa l to its side. Find the angles of the rhombus.
(A) 60° and 80°
(B) 60° and 120°
(C) 120° and 240°
(D) 100° and 120°
Answer : B

15 The perimeter of a parallelogram is 180 em. One side exceeds another by 10 cm. What are the sides of the parallelogram?
(A) 40 cm and 50 cm
(B) 45 cm each
(C) 50 cm each and 60 cm
(D) Cannot be determined.
Answer : A

16 ABCD is a parallelogram as shown in the figure. If AB = 2AD and Pis the mid-point of AB, find the measure of ∠CPD.

(A) 90°
(B) 60°
(C) 45°
(D) 135°
Answer : A

17 In a parallelogram ABCD, if AB = 2x + 5, CD = y + 1, AD = y + 5 and BC = 3x - 4, what is the ratio of AB and BC?
(A) 71 :21
(B) 12: 11
(C) 31 : 35
(D) 4 : 7 
Answer : C

18 When is the quadrilateral formed by joining the midpoints of the sides of a quadrilateral PQRS, taken in order, a rectangle?
(A) PQRS is a rectangle.
(B) PQRS is a parallelogram.
(C) Diagonals of PQRS are perpendicular.
(D) Diagonals of PQRS are equal.
Answer : C

19 The diagonals of a parallelogram ABCD intersect at O. lf ∠ BOC = 90° and ∠ BDC = 50° , find ∠ OAB.
(A) 10°
(B) 40°
(C) 50°
(D) 90°
Answer : B

20 If ABCD is an isosceles trapezium, what is ∠C eq ual to?
(A) ∠B
(B) ∠A
(C) ∠D
(D) 90°
Answer : C

21 When is the quadrilateral formed by joining the midpoints of the sides of a quadrilateral PQRS, taken in order, a rhombus?
(A) PQRS is a rhombus.
(B) PQRS is a parallelogram.
(C) Diagonals of PQRS are per-pendicular.
(D) Diagonals of PQRS are equal.
Answer : D

22 If angles P, Q, Rand 5 of the quadrilateral PQRS, taken in order, are in the ratio 3 : 7 : 6 : 4, what is PQRS?
(A) A rhombus
(B) A parallelogram
(C) A trapezium
(D) A kite
Answer : C

23 If PQ and RS are two perpendicular diameters of a circle, what is PRQS?
(A) A rectangle
(B) A trapezium
(C) A square
(D) A rhombus b ut not a square
Answer : C

24 What is the number of measurements required to construct a quadrilateral?
(A) 5
(B) 4
(C) 3
(D) 2
Answer : A

25 If the lengths of two diagonals of a rhombus are 12 cm and 16 cm, find the length of each side of the rhombus.
(A) 10 cm
(B) 14 cm
(C) 16 cm
(D) 8 cm
Answer : A

26 In a rhombus ABCD, ∠A = 60° and AB = 6 cm. Find the diagonal BD.
(A) 2√3 cm
(B) 6 cm
(C) 12 cm
(D) Insufficient data
Answer : B

27 In a parallelogram ABCD, AB = 4 em and BC = 7 em. Each of its diagonals is less than which of the following?
(A) 3 cm
(B) 4 cm
(C) 7 cm
(D) 11 cm
Answer : D

28 Which of the following is not true for a parallelogram?
(A) Opposite sides are equal.
(B) Opposite angles are equal
(C) Opposite angles are bisected by the diagonals.
(D) Diagonals bisect each ot her.
Answer : C

29 APB and CQD are parallel lines and a transversal PQ cuts them at P and Q. Which of the following is formed by the bisectors of angles APQ BPQ, CQP and PQD ?
(A) A rectangle
(B) A rhombus
(C) A square
(D) Any other parallelogram
Answer : A

30 PQRS is a quadrilateral. PR and QS intersect each other at O. ln which of the following cases is PQRS a parallelogram?
(A) ∠P = 100°, ∠Q = 80°, ∠R = 100°
(B) ∠P = 85°, ∠Q = 85°, ∠R = 95°
(C) PQ = 7 cm, QR = 7 cm, RS = 8 cm, OS= 5.2 cm
(D) OP = 6.5 cm, OQ = 6.5 cm, OR = 5.2 cm, OS= 5.2 cm
Answer : A

31 In a quadrilateral, the angles, A, B,C and D are in the ratio 1 : 2 : 3 : 4. What is the measure of the largest angle of the quadrilateral?
(A) 135°
(B) 144°
(C) 154°
(D) 108°
Answer : B

32 ABCD is a rhombus such that one of its diagonals is equal to its side. Find the measure of the angles of rhombus ABCD.
(A} 45°, 135°,45°, 135°
(B) 1 00°, 80°, 1 00°, 80°
(C) 120°, 60°, 120°, 60°
(D) 60°,60°,60°,60°
Answer : C

33 Which of the following is not a property of a rhombus?
(A) All four sides are equal
(B) Diagonals bisect each ot her.
(C) Diagonals bisect opposite angles.
(D) One angle between the diagonals is 600.
Answer : C

34 All the angles of a convex quadrilateral are congruent. However, not all sides are congruent. What type of a quadrilateral is it?
(A) Parallelogram
(B) Square
(C) Rect angle
(D) Trapezium 
Answer : C

35 In quadrilat eral ABCD, ∠A = 3B0, ∠C = 3 ∠A and L D = 4 ∠A. Find the value of ∠B.
(A) 56°
(B) 304°
(C) 52°
(D) 114°
Answer : A

36 In t he given figure, p, q and r are three parallel lines./ and mare two transversals, such that DE = 1.5 cm, EF = 3 cm. Find BC if AB = 2.5 cm.

(A) 4 cm
(B) 5.5 cm
(C) 5 cm
(D) 6 cm
Answer : C

37 ABCD is a rectangle with ∠ ABD = 40°.
Find ∠ DBC.
(A) 45°
(B) 30°
(C) 50°
(D) 35°
Answer : C

38 Find t he measure of each angle of a parallelogram, if one of its angles is 30° less than twice the smallest angle.
(A) 70°, 110°, 70°, 110°
(B) 70°, 110°, B0°, 100°
(C) 120°, 60°, 120°, 60°
(D) 100°, B0°, 100°, B0°
Answer : A

39 Which of the following pairs of angles are opposite angles of a cyclic quadrilateral?
(A) 131°, 2B°
(B) 95°, 55°
(C) 123°, 57°
(D) 64°, 52°
Answer : C

40 Two adjacent angles of rhombus are 3x - 40° and 2x + 20°. Find the measurement of the greater angle. 
(A) 160°
(B) 100°
(C) B0°
(D) 120°
Answer : B

41 If PQRS is a parallelogram, find the value of ∠Q - ∠S.
(A) 90°
(B) 120°
(C) 1B0°
(D) 0°
Answer : D

42 If the degree measures of the angles of a quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and the largest angle?
(A) 140°
(B) 150°
(C) 16B0°
(D) 1B0°
Answer : C

43 In a quadrilateral ABCD, diagonals bisect each other at right angles. If AB = BC = AD = 6 em, find the length of CD.
(A) 3 cm
(B) 6 cm
(C) 6√2 cm
(D) 12 cm
Answer : B

44 In a ΔABC, ∠A = 50°, ∠B = 60° and ∠C = 70°. Find the measures of the angles of the triangle formed by joining the midpoints of the sides of ΔABC.
(A) 40°, 60°, B0°
(B) 35°, 65°, B0°
(C) 40°, 70°, 70°
(D) 50°, 60°, 70°
Answer : D

45 In a quadrilat eral three angles are in the ratio 3 : 3 : 1 and the fourth angle is B0°.
Find the measure of the other angles.
(A) 120°, 120°, 40°
(B) 100°, 100°, 80°
(C) 110°, 110°, 60°
(D) 90°, 90°, 30°
Answer : A

46 JUMP is a square with ∠JUP = 45°. Find ∠PUM.
(A) 45°
(B) 90°
(C) 35°
(D) 15°
Answer : A

47 In ΔDEF, PQ is a line segment drawn through mid-point s of DE and DF respectively. If EF = 7.6 cm, find the length of PQ.
(A) 3.B cm
(B) 4.5 cm
(C) 7.2 cm
(D) 2.6 cm
Answer : A

48 In quadrilateral ABCD, ∠B = 90°, ∠C - ∠D = 60° and ∠A - ∠C - ∠D = 10°. Find ∠A, ∠C and ∠D.

(A) 140°, 950°, 35°
(B) 950°, 70°,65°
(C) 25°,45°, 105°
(D) 150°, 20°,35°
Answer : A

49 Two angles of a quadrilateral are 60° are 70° and other two angles are in the ratio of 8 : 15. Which of the following are the remaining two angles?
(A) 80°, 150°
(B) 90°, 140°
(C) 100°, 130°
(D) 110°, 120°
Answer : A

50 In quadrilateral ABCD. ∠A + ∠C = 140°, ∠A : ∠C = 1 : 3 and ∠B : ∠D = 5 : 6. Find the measures of ∠A, ∠B, ∠C and ∠D.
(A) 35°, 100°, 1 05°, 120°
(B) 60°, 45°, 75°, 100°
(C) 20°, 60°, 105°, 135°
(D) 45°, 35°, 90°, 110°
Answer : A

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