This set of Mathematics Problems for Class 9 focuses on “Some More Criteria for Congruence of Triangles”.

1. From the following diagram, which of the following option is true?

a) ∠A = ∠Q, ∠B = R, ∠C = ∠P

b) ∠A = ∠P, ∠B = Q, ∠C = ∠R

c) ∠A = ∠R, ∠B = P, ∠C = ∠Q

d) ∠A = ∠R, ∠B = Q, ∠C = ∠P

View Answer

Explanation: As we can see that AB = PQ, BC = QR and CA = RP, according to

**SSS rule (Theorem 7.4)**, ΔABC and PQR are congruent and hence angles of ΔABC are equal to corresponding angles of ΔPQR.

Therefore, ∠A = ∠P, ∠B = Q, ∠C = ∠R.

2. From the diagram given below, we can say that ΔABC and ΔPQR are congruent.

a) True

b) False

View Answer

Explanation: We can see in the diagram that AB = PQ, ∠ABC = ∠PQR (Right angles) and BC = PR. Therefore, according to

**RHS rule (Theorem 7.5)**, ΔABC and ΔPQR are congruent.

3. From the diagram given below, what is the true relation between ∠ABC and ∠ABD?

a) ∠ABC = ∠ABD

b) ∠ABC > ∠ABD

c) ∠ABC < ∠ABD

d) Data is insufficient

View Answer

Explanation: We can see in the diagram that AD > AC and the angles opposite to sides AD and AC are ∠ABD and ∠ABC respectively.

Therefore, according to

**theorem 7.6**, angle opposite to the longer side is larger.

Hence, ∠ABC < ∠ABD.

4. From the diagram given below, what is the true relation between three sides of the triangle?

a) AB + AC = BC

b) AB + BC = AC

c) AB + BC < AC

d) AB + BC > AC

View Answer

Explanation: According to

**theorem 7.8**, sum of any two sides of a triangle is greater than third side.

Hence, AB + BC > AC is correct.

5. From the diagram given below, which of the following option is true?

a) ΔOBA and ΔOBC are congruent

b) ΔOBA and ΔOBC are not congruent

c) ∠ABO < ∠CBO

d) ∠ABO > ∠CBO

View Answer

Explanation: We can see in the diagram that AB = BC (given),

OB = OB (same side) and AO = OC (BO is bisector of the side AC).

Therefore, according to

**SSS rule**, ΔOBA and ΔOBC are congruent.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 9**.

To practice Mathematics Problems for Class 9, __ here is complete set of 1000+ Multiple Choice Questions and Answers__.

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