CBSE Class 9 Maths Quadrilaterals MCQs

Question. The bisectors of angles of a parallelogram forms a
(A) Trapezium
(B) Rectangle
(C) Rhombus
(D) Kite
Answer : B

Question. The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O.
If ∠DAC = 32° and ∠AOB = 70°, then ∠DBC is equal to ______.
(A) 38°
(B) 86°
(C) 24°
(D) 32°
Answer : A

Question. If the angles of a quadrilateral are x, x + 20°, x – 40° and 2x. Then, the difference between greatest angle and the smallest angle is ________ .
(A) 70°
(B) 90°
(C) 80°
(D) None of these
Answer : D

Question. In a ΔABC, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm. The perimeter of the quadrilateral ARPQ is ________. A

(A) 91 cm
(B) 60 cm
(C) 51 cm
(D) 70 cm
Answer : C

Question. If a quadrilateral has two adjacent sides are equal and the opposite sides are unequal, then it is called a
(A) Parallelogram
(B) Square
(C) Rectangle
(D) Kite 
Answer : D

Question. If diagonals of a quadrilateral bisect each other at right angles, then it is a
(A) Parallelogram
(B) Rectangle
(C) Rhombus
(D) Trapezium
Answer : C

Question. If the angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Then, the measure of angles in descending order are
(A) 36°, 108°, 72° and 144°
(B) 144°, 108°, 72° and 36°
(C) 36°, 72°, 108° and 144°
(D) None of these
Answer : B

Question. The diagonals of a rectangle PQRS intersect at O. If ∠ROQ = 60°, then find ∠OSP.
(A) 70°
(B) 50°
(C) 60°
(D) 80°
Answer : C

Question. The measure of all the angles of a parallelogram, if an angle adjacent to the smallest angle is 24° less than twice the smallest angle, is
(A) 37°, 143°, 37°, 143°
(B) 108°, 72°, 108°, 72°
(C) 68°, 112°, 68°, 112°
(D) None of these
Answer : C

Question. In a quadrilateral ABCD, the line segments bisecting ∠C and ∠D meet at E. Then ∠A + ∠B is equal to ________.

(A) ∠CED
(B) (1/2)∠CED
(C) 2∠CED
(D) None of these
Answer : C

Question. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle if
(A) PQRS is a rectangle
(B) PQRS is a parallelogram
(C) Diagonals of PQRS are equal
(D) Diagonals of PQRS are at right angles
Answer : D

Question. ABCD is a rhombus with ∠ABC = 56°, then ∠ACD is equal to

(A) 90°
(B) 60°
(C) 56°
(D) 62°
Answer : D

Question. Two adjacent angles of a parallelogram are in the ratio 2 : 3. The angles are
(A) 90°, 180°
(B) 36°, 144°
(C) 72°, 108°
(D) 52°, 104°
Answer : C

Question. X, Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD.
AY and DX are joined intersecting in S; CX and BY are joined intersecting in R.
Then SXRY is a

(A) Rectangle D
(B) Rhombus
(C) Parallelogram
(D) Square
Answer : B

Question. D and E are the mid-points of the sides AB and AC, respectively of ΔABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
(A) ∠DAE = ∠EFC
(B) AE = EF
(C) DE = EF
(D) ∠ADE = ∠ECF
Answer : C

Question. In given figure, ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ = (1/4)AC and PQ produced meet BC at R, then

(A) CR = (1/3)CB
(B) CR = RB
(C) CR = (1/2)RB
(D) None of these
Answer : B

Question. In the given figure, if ABCD is a rectangle and P, Q are the mid-points of AD, DC respectively. Then, the ratio of lengths PQ and AC is equal to

(A) 1 : 1
(B) 1 : 2
(C) 2 : 1
(D) 3 : 2
Answer : B

Question. ABCD is a parallelogram. If AB is produced to E such that ED bisects BC at O. Then which of the following is correct?
(A) AB = OE
(B) AB = BE
(C) OE = OC
(D) None of these
Answer : B

Question. If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form
(A) Kite
(B) Rhombus
(C) Rectangle
(D) Trapezium
Answer : C

Question. In figure, E and F are the mid-points of sides AB and AC of a DABC. If AB = 5 cm, BC = 5 cm and AC = 6 cm, then EF is equal to

(A) 3 cm
(B) 2.5 cm
(C) 4 cm
(D) None of these
Answer : B

Question. Study the statements carefully.
Statement-1 : If a sum of a pair of opposite angles of a quadrilateral is 180°, the quadrilateral is cyclic.
Statement-2 : A line drawn through mid point of a side of a triangle, parallel to another side equal to third side. Which of the following options holds?
(A) Both Statement-1 and Statement-2 are true.
(B) Statement-1 is true but Statement-2 is false.
(C) Statement-1 is false but Statement-2 is true.
(D) Both Statement-1 and Statement-2 are false.
Answer : B

Question. Read the statements carefully and state ‘T’ for true and ‘F’ for false.
(i) Diagonals of a parallelogram are perpendicular to each other.
(ii) All four angles of a quadrilateral can be obtuse angles.
(iii) If all sides of a quadrilateral are equal, then it is a rhombus.
     (i)       (ii)     (iii)
(A) T        F        F
(B) F        F        T
(C) F        T        T
(D) F        F        F
Answer : B

Question. By using a given figure of quadrilateral ABCD, match the following

(A) (P)→(1), (Q)→(2), (R)→(3), (S)→(4)
(B) (P)→(2), (Q)→(1), (R)→(4), (S)→(3)
(C) (P)→(3), (Q)→(1), (R)→(2), (S)→(4)
(D) (P)→(4), (Q)→(3), (R)→(1), (S)→(2)
Answer : B

Question. Fill in the blanks.
(a) If consecutive sides of a parallelogram are equal then it is necessarily a P .
(b) The figure formed by joining the mid-points of consecutive sides of a quadrilateral is Q .
(c) If the diagonals of a parallelogram are equal and perpendicular to each other, it is a R .
           P                       Q                           R
(A) Square           Parallelogram           Rhombus
(B) Kite                Rhombus                  Square
(C) Rhombus       Rectangle                 Rectangle
(D) Rhombus       Parallelogram           Square
Answer : D

Question. If the sides BA and DC of quadrilateral ABCD are produced as shown in the given figure, then

(A) x + y = a + b
(B) x – y = a – b
(C) x-y/2 = a - b
(D) 2(x + y) = a + b
Answer : A

Question. The bisectors of angles of a parallelogram form a :
(a) trapezium
(b) rectangle
(c) rhombus
(d) kite

Question. The angles of a quadrilaterals are in the ratio 3 : 4 : 5 : 6. The respective angles of the quadrilaterals are
(a) 60⁰, 80⁰, 100⁰, 120⁰
(b) 120⁰, 100⁰, 80⁰, 60⁰
(c) 120⁰, 60⁰, 80⁰, 100⁰
(d) 80⁰, 100⁰, 120⁰, 60⁰.

Question. If diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a:
(a) parallelogram
(b) square
(c) rhombus
(d) trapezium

Question. If in rectangle ABCD, diagonal AC bisects <C, then ABCD is a:
(a) parallelogram
(b) square
(c) rhombus
(d) trapezium

Question. The line segment joining the midpoints of two sides of a triangle is parallel to the third side and ________ of it.
(a) half
(b) one third
(c) one fourth
(d) equal

Question. Line segment joining the mid points of the opposite sides of a quadrilateral _________ each other.
(a) trisect
(b) bisect
(c) coincide
(d) none of these.

Question. Three angles of a quadrilateral are 75⁰, 90⁰ and 75⁰. The fourth angle is
(a) 90⁰
(b) 95⁰
(c) 105⁰
(d) 120⁰

Question. A diagonal of a rectangle is inclined to one side of the rectangle at 250. The acute angle between the diagonals is
(a) 55⁰
(b) 50⁰
(c) 40⁰
(d) 25⁰

Question. ABCD is a rhombus such that <ACB = 400, then <ADB =
(a) 45⁰
(b) 50⁰
(c) 40⁰
(d) 60⁰

Question. The quadrilateral formed by joining the midpoints of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if
(a) PQRS is a rectangle
(b) PQRS is an parallelogram
(c) diagonals of PQRS are perpendicular
(d) diagonals of PQRS are equal.

Question. The quadrilateral formed by joining the midpoints of the sides of a quadrilateral PQRS, taken in order, is a rhombus, if
(a) PQRS is a rhombus
(b) PQRS is an parallelogram
(c) diagonals of PQRS are perpendicular
(d) diagonals of PQRS are equal.

Question. If angles A, B, C and D of the quadrilateral ABCD, taken in order are in the ratio 3:7:6:4, then ABCD is a
(a) parallelogram
(b) kite
(c) rhombus
(d) trapezium

Question. If bisectors of If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a
(a) parallelogram
(b) rectangle
(c) rhombus
(d) quadrilateral whose opposite angles are supplementary.

Question. If APB and CQD are two parallel lines then bisectors of the angles APQ. BPQ, CQP and PQD form a
(a) parallelogram
(b) square
(c) rhombus
(d) rectangle

Question. The figure obtained the midpoints of the sides of the sides of a rhombus, taken in order is a
(a) parallelogram
(b) square
(c) rhombus
(d) rectangle

Question. D and E are the midpoints of the sides AB and AC of ΔABC and O is any point on side BC. O is joined to A. If P and Q are the midpoints of OB and OC respectively, then DEQP is a
(a) parallelogram
(b) square
(c) rhombus
(d) rectangle

Question. The quadrilateral formed by joining the midpoints of the sides of a quadrilateral PQRS, taken in order, is a square only if
(a) PQRS is a rhombus
(b) diagonals of PQRS are equal and perpendicular
(c) diagonals of PQRS are perpendicular
(d) diagonals of PQRS are equal.

Question. The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32⁰ and ∠AOB = 70⁰, then ∠DBC is equal to
(a) 24⁰
(b) 86⁰
(c) 38⁰
(d) 32⁰

Question. Which of the following is not true for a parallelogram?
(a) opposite sides are equal
(b) opposite angles are bisected by the diagonals
(c) opposite angles are equal
(d) diagonals bisect each other.

Question. D and E are the midpoints of the sides AB and AC of ΔABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional informationwhich is 
(a) ∠DAE = ∠EFC
(b) AE = EF
(c) DE = EF
(d) ∠ADE = ∠ECF

Question. The bisectors of any two adjacent angles of a parallelogram intersect at
(a) 45⁰
(b) 30⁰
(c) 90⁰
(d) 60⁰

Question. The bisectors of the angles of a parallelogram enclose a
(a) parallelogram
(b) square
(c) rhombus
(d) rectangle

Question. ABCD is a parallelogram and E and F are the centroid of triangle ABD and BCD respectively, then EF =
(a) AE
(b) BE
(c) CE
(d) DE

Question. ABCD is a parallelogram, M is the midpoint of BD and BM bisects ∠B, then ∠AMB =
(a) 45⁰
(b) 75⁰
(c) 90⁰
(d) 60⁰

Question. Given four points A, B, C, D such that three points A, B, C are collinear. By joining these points in order, we get
(a) a straight line
(b) a triangle
(c) quadrilateral
(d) none of these

Question. In quadrilateral ABCD, AB = BC and CD = DA, then the quadrilateral is a
(a) parallelogram
(b) rhombus
(c) kite
(d) trapezium

Question. Given a triangular prism, then what can we conclude about the lateral faces.
(a)faces are rectangular
(b) faces are parallelogram
(c) faces are trapeziums
(d) square

Question. The bisectors of the angles of parallelogram enclose a
(a) parallelogram
(b) rhombus
(c) rectangle
(d) square

Question. Which if the following quadrilateral a rhombus?
(a) diagonals bisect each other
(b) all the four sides are equal
(c) diagonals bisect opposite angles
(d) one angle between the diagonals is 600.

Question. Consecutive angles of parallelogram are
(a) equal
(b) supplementary
(c) complementary
(d) none of these

Question. Given a rectangle ABCD and P, Q, R, S midpoints of AB, BC, CD and DA respectively. Length of diagonal of rectangle is 8 cm, the quadrilateral PQRS is
(a) parallelogram with adjacent sides 4 cm
(b) rectangle with adjacent sides 4 cm
(c) rhombus with side 4 cm
(d) square with side 4 cm

Question. In parallelogram ABCD, bisectors of angles and B intersect each other at O. The value of AOB is:
(a) 30⁰
(b) 60⁰
(c) 90⁰
(d) 120⁰

Question. If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is
(a) 108⁰
(b) 54⁰
(c) 72⁰
(d) 81⁰

Question. If the degree measures of the angles of quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and largest angle?
(a) 140⁰
(b) 150⁰
(c) 168⁰
(d) 180⁰

Question. In the given figure ABCD is a parallelogram, what is the sum of the angle x, y and z?
(a) 140⁰
(b) 150⁰
(c) 168⁰
(d) 180⁰

Question. In the above figure ABCD is a rhombus, then the value of x is
(a) 40⁰
(b) 50⁰
(c) 60⁰
(d) 80⁰

Question. In the below figure ABCD is a rhombus, then the value of x is
(a) 20⁰
(b) 25⁰
(c) 30⁰
(d) 50⁰

Question. ABCD is a parallelogram and AB = 12cm, AD = 8 cm then perimeter of parallelogram ABCD is
(a) 20 cm
(b) 40 cm
(c) 60 cm
(d) 80 cm

Question. In parallelogram CARS, mÐC = 5x - 20 and mÐA = 3x + 40. Find the value of x.
(a) 15
(b) 20
(c) 30
(d) 130 

Question. If two consecutive sides of a rhombus are represented by 3x - 6 and x + 14, then the perimeter of the rhombus is
(a) 10
(b) 24
(c) 70
(d) 96

Question. Points A, B, C, and D are midpoints of the sides of square JETS. If the area of JETS is 36, the area of ABCD is
(a) 9 √2
(b) 18√2
(c) 9
(d) 18

Question. In the accompanying above diagram of rectangle ABCD, m
(a) 36°
(b) 60°
(c) 84°
(d) 90°

Question. A quadrilateral must be a parallelogram if one pair of opposite sides is
(a) congruent, only.
(b) parallel and the other pair of opposite sides is congruent.
(c) congruent and parallel.
(d) parallel only

Question. The perimeter of a rhombus is 60. If the length of its longer diagonal measures 24, the length of the shorter diagonal is
(a) 20
(b) 18
(c) 15
(d) 9

Question. Find the perimeter of a rhombus whose diagonals measure 12 and 16.
(a) 10
(b) 20
(c) 40
(d) 80

Question. Which statement is true about all parallelograms?
(a) The diagonals are congruent.
(b) The area is the product of two adjacent sides.
(c) The opposite angles are congruent.
(d) The diagonals are perpendicular to each other.

Question. Which property is true for all trapezoids?
(a) Only two opposite sides are parallel.
(b) Consecutive angles are supplementary.
(c) The base angles are congruent.
(d) All angles are equal.

Question. In the diagram at the right, ABCD is a square, diagonal BD is extended through D to E. AD = DE and AE is drawn as given in figure. What is m

(a) 22.5
(b) 45.0
(c) 112.5
(d) 135.0 

Question. In the above right sided diagram of rhombus ABCD, m
(a) 35°
(b) 70°
(c) 110°
(d) 140°

Question. In rectangle DATE, diagonals DT and AE intersect at S. If AE = 40 and ST = x + 5, find the value of x.
(a) 10
(b) 18
(c) 15
(d) 20

Question. A parallelogram must be a rectangle if its diagonals
(a) bisect each other.
(b) bisect the angles to which they are drawn.
(c) are perpendicular to each other.
(d) are congruent. 

Question. Three angles of a quadrilateral are 75⁰ , 90⁰ and 75⁰. The fourth angle is
(A) 90⁰
(B) 95⁰
(C) 105⁰
(D) 120⁰

Question. A diagonal of a rectangle is inclined to one side of the rectangle at 25؛. The acute angle between the diagonals is
(A) 55⁰
(B) 50⁰
(C) 40⁰
(D) 25⁰

Question. ABCD is a rhombus such that (A) 40⁰
(B) 45⁰
(C) 50⁰
(D) 60⁰0. Then

Question. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if
(A) PQRS is a rectangle
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal.

Question. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rhombus, if
(A) PQRS is a rhombus
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal.

Question. If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is a
(A) rhombus
(B) parallelogram
(C) trapezium
(D) kite

Question. If bisectors of
(A) rectangle
(B) rhombus
(C) parallelogram
(D) quadrilateral whose opposite angles are supplementary

Question. If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form
(A) a square
(B) a rhombus
(C) a rectangle
(D) any other parallelogram

Question. The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is
(A) a rhombus
(B) a rectangle
(C) a square
(D) any parallelogram

Question. D and E are the mid-points of the sides AB and AC of <ABC and O is any point on side BC. O is joined to A. If P and Q are the mid-points of OB and OC respectively, then DEQP is
(A) a square
(B) a rectangle
(C) a rhombus
(D) a parallelogram