**MCQs on Class 9 Quadrilaterals**

**1) The quadrilateral whose all its sides are equal and angles are equal to 90 degrees, it is called:**

a. Rectangle

b. Square

c. Kite

d. Parallelogram

Answer:** b**

**2) The sum of all the angles of a quadrilateral is equal to:**

a. 180°

b. 270°

c. 360°

d. 90°

Answer:** c**

**3) A trapezium has:**

a. One pair of opposite sides parallel

b. Two pair of opposite sides parallel to each other

c. All its sides are equal

d. All angles are equal

Answer:** a**

Explanation: A trapezium has only one pair of opposite sides parallel to each other, and the other two sides are non-parallel.

**4) A rhombus can be a:**

a. Parallelogram

b. Trapezium

c. Kite

d. Square

Answer:** d**

**5) A diagonal of a parallelogram divides it into two congruent:**

a. Square

b. Parallelogram

c. Triangles

d. Rectangle

Answer:** c**

**6) In a parallelogram, opposite angles are:**

a. Equal

b. Unequal

c. Cannot be determined

d. None of the above

Answer:** a**

**7) The diagonals of a parallelogram:**

a. Equal

b. Unequal

c. Bisect each other

d. Have no relation

Answer:** c**

Explanation: The diagonals of a parallelogram intersect each other at 90 degrees.

**8) Each angle of the rectangle is:**

a. More than 90°

b. Less than 90°

c. Equal to 90°

d. Equal to 45°

Answer:** c**

Explanation: Let ABCD is a rectangle, and ∠A = 90°

AD || BC and AB is a transversal

∠ A + ∠ B = 180° (Interior angles on the same side of the transversal)

∠ A = 90°

So, ∠ B = 180° – ∠ A = 180° – 90° = 90°

Now, ∠ C = ∠ A and ∠ D = ∠ B (Opposite angles of the parallelogram)

So, ∠ C = 90° and ∠ D = 90°

Hence all sides are equals to 90°.

**9) The angles of a quadrilateral are in the ratio 4: 5: 10: 11. The angles are:**

a. 36°, 60°, 108°, 156°

b. 48°, 60°, 120°, 132°

c. 52°, 60°, 122°, 126°

d. 60°, 60°, 120°, 120°

Answer:** b**

Explanation: Let x be the common angle among all the four angles of a quadrilateral.

As per angle sum property, we know:

4x+5x+10x+11x = 360°

30x = 360°

x = 12°

Hence, angles are

4x = 4 (12) = 48°

5x = 5 (12) = 60°

10x = 10 (12) = 120°

11x = 11 (12) = 132°

**10) If ABCD is a trapezium in which AB || CD and AD = BC, then:**

a. ∠A = ∠B

b. ∠A > ∠B

c. ∠A < ∠B

d. None of the above

Answer:** a**

Explanation: Draw a line through C parallel to DA intersecting AB produced at E.

CE = AD (Opposite sides)

AD = BC (Given)

BC = CE

⇒ ∠CBE = ∠CEB

also,

∠A + ∠CBE = 180° (Angles on the same side of transversal and ∠CBE = ∠CEB)

∠B + ∠CBE = 180° ( As Linear pair)

⇒ ∠A = ∠B