CBSE Class 8 Mathematics Understanding Quadrilaterals MCQs

Various Types of Quadrilaterals

1. Quadrilateral: A closed figure bounded by four line segments is called a quadrilateral.
2. Types of quadrilaterals.
a) Parallelogram: In a parallelogram
i) the opposite sides are equal
ii) the opposite angles are equal
iii) each diagonal bisects the other.
b) Rectangle: A parallelogram is a rectangle if each of its angles is a right angle. A rectangle obeys all the properties of a parallelogram.
c) Square: A rectangle having all its sides equal is called a square.
d) Rhombus: A rectangle having all its sides equal is called a square.
e) Kite: Kite is a quadrilateral formed by two isosceles triangle standing on the opposite sides of a common base.
f) Trapezium: A quadrilateral in which one pair of opposite sides are parallel is called a trapezium.
Note: If the non-parallel sides of a trapezium are equal, it is called an isosceles trapezium 

Venn - diagram of Quadrilaterals

Q = set of all quadrilaterals in a given plane
T = set of all trapeziums in the given plane
P = set of all parallelograms in the given plane
S = set of all squares in the given plane
R = set of all rectangles in the given plane
H = set of all rhombuses in the given plane
K = set of all kites in the given plane. 

Question. The perimeter of a parallelogram is 180 cm. One side exceeds another by 10 cm. The sides of the parallelogram are
(A) 40 cm, 50 cm
(B) 45 cm each
(C) 50 cm each
(D) cannot be determined

Answer: A

Question. One of the diagonals of a rhombus is equal to a side of the rhombus. The angles of the rhombus are
(A) 60° and 80°
(B) 60° and 120°
(C) 120° and 240°
(D) 100° and 120°

Answer: B

Question. In the quadrilatral ABCD, the diagonals AC and BD are equal and perpendicular to each other. Then ABCD is a
(A) square
(B) parallelogram
(C) rhombus
(D) trapezium

Answer: A

Question. ABCD is a parallelogram as shown in figure. IF AB = 2AD and P is midpoint of AB, then <CPD is equal to 

(A) 90°
(B) 60°
(C) 45°
(D) 135°

Answer: A

Question. In a parallelogram ABCD, if AB = 2x + 5, CD = y + 1, AD = y + 5 and BC = 3x – 4 then ratio of AB : BC
(A) 71 : 21
(B) 12 : 11
(C) 31 : 35
(D) 4 : 7

Answer: C

Question. If ABCD is an isosceles trapezium, ∠C is equal to
(A) ∠B
(B) ∠A
(C) ∠D
(D) 90°

Answer: C

Question. The diagonals of a parallelogram ABCD intesect at O. If ∠BOC - 90° and ∠BDC = 50°, then ∠AOB is
(A) 10°
(B) 40°
(C) 50°
(D) 90°

Answer: B

Question. A diagonal of a rectangle is inclined to one side of the rectangle at 25°. the acute angle between the diagonals is
(A) 25°
(B) 40°
(C) 50°
(D) 55°

Answer: C

Question. ABCD is a rhombus. IF ∠ACB = 40°, then ∠ADB is
(A) 40°
(B) 45°
(C) 50°
(D) 60°

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 perpendicular
(D) diagonals sof PQRS is equal

Answer: C

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

Answer: C

Question. If PQ and RS are two perpendicular diameters of a circle, then PQRS is a
(A) rectangle
(B) trapezium
(C) square
(D) rhombus but not square

Answer: C

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

Answer: D

Question. AB and CD are diameters. Then ACBD is 

(A) square
(B) trapezium
(C) isosceles trapezium
(D) rectangle

Answer: D

Question. ABCD is a square E, F, G, H are the mid-mid-points of the four sides. Then the figure EFGH is
(A) square
(B) rectangle
(C) trapezium
(D) parallelogram

Answer: A

Question. If a quadrilateral has two adjacent sides equal and the other two sides equal it is called
(A) parallelogram
(B) square
(C) rectangle
(D) kite

Answer: D

Question. Choose the correct statement:
(A) The diagonals of a parallelogram are equal
(B) The diagonals of a rectangle are perpendicular to each other
(C) If the diagonals of a quadrilateral intersect at right angles, it is not necessary a rhombus
(D) Every quadrilateral is either a trapezium or a parallelogram or a kite.

Answer: C

Question. If two adjacent angles of a parallelogram are in the ratio 3:2, then the measure of the angles are
(A) 108°, 72°
(B) 72°, 36°
(C) 100°, 80°
(D) 144°, 36°

Answer: A

Question. ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must be
(A) square
(B) rectangle
(C) parallelogram
(D) The angle

Answer: C

Question. ABCD is a parallelogram. The angle bisectors of ∠A and ∠D meet at O. The measure of ∠AOD is
(A) 45°
(B) 90°
(C) dependent on the angles A and D
(D) cannot be determined from given data

Answer: B

Question. The diameter of circumcircle of a rectangle is 10 cm and breath of the rectanelge is 6 cm. Its length i s
(A) 6 cm
(B) 5 cm
(C) 8 cm
(D) none

Answer: C

Question. ABCD is a quadrilateral. AB = BC = CD = DA and ∠A = ∠B = ∠C = ∠D = 90°. Then ABCD can be called ABCD can be called
(A) qrhombus
(B) square
(C) parallelogram
(D) all of the foregoing

Answer: D

Question. The sum of the angles of a quadrilateral is
(A) 180°
(B) 360°
(C) 270°
(D) depends on the quadrilateral

Answer: B

Question. RSTU is a parallelogram as shown in the figure below. Then the shown angle x and y are related 

(A) x = y
(B) x < y
(C) x > y
(D) cannot be determined from given data

Answer: D

Question. ABCD and MNOP are quadrilaterals as shown in the figure below. Then 

(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) none of the forgoing

Answer: B

Question. A parallelogram which has equal diagonals is a
(A) square
(B) rectangle
(C) rhombus
(D) none

Answer: B

Question. IF ABCD is a parallelogram, then ∠A – ∠C is
(A) 180°
(B) 0°
(C) 360°
(D) 90°

Answer: D

Question. In a suqare ABCD the diagonals bisect at O. Then triangle AOB is
(A) an equilateral triangle
(B) an isosceles but not a right angled
(C) a right angled but not an isosceles triangle
(D) an isosceles right angled triangle

Answer: A

Question. The angle between two altitudes of a parallelogram ABCD through the vertex D which is obtuse angle, is 60°. Then ∠ABC is
(A) 60°
(B) 90°
(C) 120°
(D) 140°

Answer: C

Question. To construct a parallelogram, the minimum number of measurements required is
(A) 2
(B) 3
(C) 4
(D) 1

Answer: B

Question. If angles P, Q, R and S of the quadrilateral PQRS taken in order, are in the ratio 3 : 7 : 6 : 4, then PQRS is a
(A) Rhombus
(B) Parallelogram
(C) Trapezium
(D) Kite

Answer: C

Question. ABCD is parallelogram AC ⊥ BD and ∠ACD = 30°, then ∠ABD is
(A) 45°
(B) 60°
(C) 90°
(D) 120°

Answer: B

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) PQRS is a rectangle

Answer: D

Question. If the lengths of two diagonals of a rhombus is 12 cm and 16 cm, then the length of each side of the rhombus is
(A) 10 cm
(B) 14 cm
(C) cannot be determined
(D) 5 cm

Answer: A

Question. Three angles of quadrilateral are in the ratio 3 : 4 : 5. The difference of the least and the greatest of these is 45°. All the four angles of the quadrilateral are
(A) 63°, 84°, 105°, 108°
(B) 60°, 75°, 120°, 105°
(C) 65°, 80°, 100°, 110°
(D) 85°, 95°, 100°, 130°

Answer: A

Question. PQRS is a rhombus. The value of perimeter if PR = 10 cm and QS = 24 cm is
(A) 50 cm
(B) 51 cm
(C) 52 cm
(D) 53 cm

Answer: C

Question. The given figure HOPE is a parallelogram. The relation between x, y and z is
(A) x = y + z
(B) y + z – x = 180°
(C) x + y – z = 180°
(D) x + y = 180° – z

Answer: D

Question. ABCD is a rhombus in which the altitide from D to side AB bisects AB. Then ∠A and ∠B are
(A) 60°, 120°
(B) 120°, 60°
(C) 80°, 100°
(D) 100°, 80°

Answer: A

Question. The sum of the measures of the external angles of any polygon is
(A) 180°
(B) 360°
(C) 540°
(D) Depends on the number of sides

Answer: B

Question. The number of sides of a regular polygon whose each exterior angle has a measure of 45° is
(A) 4
(B) 6
(C) 8
(D) 10
Answer: C

Question. If ABCD is an isosceles trapezium, ∠C is equal to
(A) ∠B
(B) ∠A
(C) ∠D
(D) 90°

Answer: C

Question. If a pair of opposite sides of a quadrilateral are equal and parallel it is
(A) kite
(B) trapezium
(C) parallelogram
(D) none of these

Answer: C

Question. In a parallelogram ABCD, if ∠A = 45°, then the other angles are
(A) 45°, 120°, 120°
(B) 45°, 135°, 135°
(C) 60°, 135°, 135°
(D) 60°, 120°, 120°

Answer: B

Question. The sum of the angles of quadrilateral is
(A) 180°
(B) 360°
(C) 270°
(D) Depends on the quadrilateral

Answer: B

Question. In the given figure, line RT is drawn parallel to SQ. If ∠QPS = 100°, ∠PQS = 40°, ∠PSR = 85° and ∠QRS = 70°, then ∠QRT is 

(A) 45°
(B) 65°
(C) 85°
(D) 90°

Answer: B

Question. Match the following:
1. Rectangle         (p) A quadrilateral having its opposite sides parallel.
2. Square             (q) A parallelogram having its opposite sides equal and one angle measuring 90°
3. Parallelogram   (r) A parallelogram having all sides equal and one angle measuring 90°
4. Rhombus          (s) A quadrilateral in which a pair of opposite sides are parallel
5. Trapezium         (t) A parallelogram having all sides equal
(A) 1t 2s 3r 4p 5q
(B) 1p 2q 3r 4s 5t
(C) 1r 2q 3t 4p 5s
(D) 1q 2r 3p 4t 5s

Answer: D

Question. Four angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. The greatest angle is
(A) 125°
(B) 75°
(C) 135°
(D) 120°

Answer: C

Question. Diagonals of a rhombus bisect each other at
(A) Acute angle
(B) Obtuse angle
(C) Right angle
(D) ½ right angle

Answer: C

Question. Which of the following statements is true?
(A) The diagonals of a rectangle are perpendicular
(B) The diagonals of a rhombus are equal
(C) Every square is a rhombus
(D) Every rhombus is a square

Answer: C

Question. In rectangle ABCD, AB = 25 cm and BC = 15 cm. In what ratio does the bisector of ∠C divides AB?
(A) 1 : 3
(B) 2 : 3
(C) 3 : 4
(D) 1 : 4

Answer: B

Question. In the figure, P is a point in the interior of ∠AOB and ∠AOB = 36°, If PM ⊥ OA and PN ⊥ OB. Then x is 

(A) 144°
(B) 90°
(C) 216°
(D) 45°

Answer: C

Question. A trapezium in which non parallel sides are equal is side to be
(A) right trapezium
(B) equilateral trapezium
(C) isosceles trapezium
(D) none of these

Answer: C

Question. If ABCD is a parallelogram, then LA – LC is
(A) 180°
(B) 0°
(C) 360°
(D) 90°

Answer: B

Question. If one of the angles measures more than 180° in a quadrilateral, then quadrilateral is known as
(A) A parallelogram
(B) A concave quadrilateral
(C) A convex quadrilateral
(D) A trapezium

Answer: B

Question. The ratio of sides of a parallelogram is 3 : 5 and the perimeter is 48 cm, then the sides of the parallelogram are
(A) 9 cm, 12 cm
(B) 9 cm, 15 cm
(C) 10 cm, 12 cm
(D) 8 cm, 15 cm

Answer: A

Question: The perimeter of a parallelogram is 180 cm. One side exceeds another by 10 cm. The sides of the parallelogram are
a) 40 cm, 50 cm
b) 50 cm each
c) 45 cm each
d) cannot be determined