## ICSE Class 9 Triangles MCQ New Pattern

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### ICSE Class 9 Triangles MCQ HERE

**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 the largest angle will be the longest one.

**11) Which of the following is not a criterion for congruence of triangles?**

(a) SAS

(b) ASA

(c) SSA

(d) SSS

Answer: **c**

Explanation:

SSA is not a criterion for the congruence of triangles. Whereas SAS, ASA and SSS are the criteria for the congruence of triangles.

**12) In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are**

(a) Isosceles and congruent

(b) Isosceles but not congruent

(c) Congruent but not isosceles

(d) Neither congruent nor isosceles

Answer: **b**

Explanation:

Consider two triangles, ABC and PQR. If the sides AB = AC and ∠C = ∠P and ∠B = ∠Q, then the two triangles are said to be isosceles, but they are not congruent.

**13) In ∆ PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is**

(a) 2 cm

(b) 2.5 cm

(c) 4 cm

(d) 5 cm

Answer: **c**

Explanation:

Given that, in a triangle PQR, ∠R = ∠P.

Since, ∠R = ∠P, the sides opposite to the equal angles are also equal.

Hence, the length of PQ is 4 cm.

**14) If AB = QR, BC = PR and CA = PQ, then**

(a) ∆ PQR ≅ ∆ BCA

(b) ∆ BAC ≅ ∆ RPQ

(c) ∆ CBA ≅ ∆ PRQ

(d) ∆ ABC ≅ ∆ PQR

Answer: **c**

Explanation:

Consider two triangles ABC and PQR.

Given that, AB = QR, BC = PR and CA = PQ.

By using Side-Side-Side (SSS rule),

We can say, ∆ CBA ≅ ∆ PRQ.

**15) If ∆ ABC ≅ ∆ PQR, then which of the following is not true?**

(a) AC = PR

(b) BC = PQ

(c) QR = BC

(d) AB = PQ

Answer: **b**

Explanation:

Given that, ∆ ABC ≅ ∆ PQR

Hence, AB = PQ

BC = QR

AC =PR

Thus, BC = PQ is not true, if ∆ ABC ≅ ∆ PQR.

**16) In ∆ ABC, BC = AB and ∠B = 80°. Then ∠A is equal to**

(a) 40°

(b) 50°

(c) 80°

(d) 100°

Answer: **b**

Explanation: In a triangle, ABC, BC = AB and ∠B = 80°.

Thus, the given triangle is an isosceles triangle.

By using the angle sum property of a triangle, we get

x + 80°+x = 180°

2x+ 80°= 180°

2x = 180°- 80°

2x = 100°

x = 100°/2 = 50°

Therefore, ∠A = 50°.

**17) Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be**

(a) 3.4 cm

(b) 3.6 cm

(c) 3.8 cm

(d) 4.1 cm

Answer: **a**

Explanation: If two sides of a triangle are of lengths 5 cm and 1.5 cm, then the length of the third side of the triangle cannot be 3.4 cm. Because the difference between the two sides of a triangle should be less than the third side.

**18) In ∆ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to**

(a) 40°

(b) 50°

(c) 80°

(d) 130°

Answer: **b**

Explanation:

Given that, in a triangle ABC, AB = AC and ∠B = 50°.

Since the given triangle is an isosceles triangle, the angles opposite to the equal sides are also equal. Hence, ∠C = 50°.

**19) In ∆ PQR, if ∠R > ∠Q, then**

(a) QR < PR

(b) PQ < PR

(c) PQ > PR

(d) QR > PR

Answer: **c**

Explanation: In a triangle PQR, if ∠R > ∠Q, then PQ > PR, because the side opposite to the greater angle is longer.

**20) It is given that ∆ ABC ≅ ∆ FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true? **

(a) DF = 5 cm, ∠F = 60°

(b) DF = 5 cm, ∠E = 60°

(c) DE = 5 cm, ∠E = 60°

(d) DE = 5 cm, ∠D = 40

Answer: **b**

Explanation:

Given that, ∆ ABC ≅ ∆ FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°.