# Mathematics Questions and Answers – Some More Criteria for Congruence of Triangles

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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

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

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

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

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

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. 