**MCQs on Class 9 Triangles**

Solve the MCQs

**1) In triangle ABC, if AB=BC and ∠B = 70°, ∠A will be:**

a. 70°

b. 110°

c. 55°

d. 130°

Answer:** c**

Explanation: Given,

AB = BC

Hence, ∠A=∠C

And ∠B = 70°

By angle sum property of triangle we know:

∠A+∠B+∠C = 180°

2∠A+∠B=180°

2∠A = 180-∠B = 180-70 = 110°

∠A = 55°

**2) For two triangles, if two angles and the included side of one triangle are equal to two angles and the included side of another triangle. Then the congruency rule is:**

a. SSS

b. ASA

c. SAS

d. None of the above

Answer:** b**

**3) A triangle in which two sides are equal is called:**

a. Scalene triangle

b. Equilateral triangle

c. Isosceles triangle

d. None of the above

Answer:** c**

**4) The angles opposite to equal sides of a triangle are:**

a. Equal

b. Unequal

c. supplementary angles

d. Complementary angles

Answer:** a**

**5) If E and F are the midpoints of equal sides AB and AC of a triangle ABC. Then:**

a. BF=AC

b. BF=AF

c. CE=AB

d. BF = CE

Answer:** d**

Explanation: AB and AC are equal sides.

AB = AC (Given)

∠A = ∠A (Common angle)

AE = AF (Halves of equal sides)

∆ ABF ≅ ∆ ACE (By SAS rule)

Hence, BF = CE (CPCT)

**6) ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Then:**

a. BE>CF

b. BE<CF

c. BE=CF

d. None of the above

Answer:** c**

Explanation:

∠A = ∠A (common arm)

∠AEB = ∠AFC (Right angles)

AB = AC (Given)

∴ ΔAEB ≅ ΔAFC

Hence, BE = CF (by CPCT)

**7) If ABC and DBC are two isosceles triangles on the same base BC. Then:**

a. ∠ABD = ∠ACD

b. ∠ABD > ∠ACD

c. ∠ABD < ∠ACD

d. None of the above

Answer:** a**

Explanation: AD = AD (Common arm)

AB = AC (Sides of isosceles triangle)

BD = CD (Sides of isosceles triangle)

So, ΔABD ≅ ΔACD.

∴ ∠ABD = ∠ACD (By CPCT)

**8) If ABC is an equilateral triangle, then each angle equals to:**

a. 90°

B.180°

c. 120°

d. 60°

Answer:** d**

Explanation: Equilateral triangle has all its sides equal and each angle measures 60°.

AB= BC = AC (All sides are equal)

Hence, ∠A = ∠B = ∠C (Opposite angles of equal sides)

Also, we know that,

∠A + ∠B + ∠C = 180°

⇒ 3∠A = 180°

⇒ ∠A = 60°

∴ ∠A = ∠B = ∠C = 60°

**9) If AD is an altitude of an isosceles triangle ABC in which AB = AC. Then:**

a. BD=CD

b. BD>CD

c. BD<CD

d. None of the above

Answer:** a**

Explanation: In ΔABD and ΔACD,

∠ADB = ∠ADC = 90°

AB = AC (Given)

AD = AD (Common)

∴ ΔABD ≅ ΔACD (By RHS congruence condition)

BD = CD (By CPCT)

**10) In a right triangle, the longest side is:**

a. Perpendicular

b. Hypotenuse

c. Base

d. None of the above

Answer:** b**

Explanation: In triangle ABC, right-angled at B.

∠B = 90

By angle sum property, we know:

∠A + ∠B + ∠C = 180

Hence, ∠A + ∠C = 90

So, ∠B is the largest angle.

Therefore, the side (hypotenuse) opposite to largest angle will be longest one.