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In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆ PQR should be equal to side BC of ∆ ABC so that the two triangles are congruent? Give reason for your answer

Solution:

It is given that

In triangles ABC and PQR,

∠A = ∠Q

∠B = ∠R

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆ PQR should be equal to side BC of ∆ ABC so that the two triangles are congruent? Give reason for your answer

We know that

When two angles are equal in triangles ABC and PQR, then third angle of one triangle will be equal to the third angle of the other triangle

∠C = ∠P

PR = BC

From ASA criterion

ASA congruence criterion states that, "if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles will be congruent".

∆ ABC ≅ ∆ PQR

Therefore, the side PR of ∆ PQR should be equal to side BC of ∆ ABC so that the two triangles are congruent.

✦ Try This: In triangles DEF and XYZ, ∠D = ∠Y and ∠E = ∠Z. Which side of ∆ XYZ should be equal to side EF of ∆ DEF so that the two triangles are congruent? Give reason for your answer.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

NCERT Exemplar Class 9 Maths Exercise 7.2 Problem 2

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆ PQR should be equal to side BC of ∆ ABC so that the two triangles are congruent? Give reason for your answer

Summary:

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Side PR of ∆ PQR should be equal to side BC of ∆ ABC so that the two triangles are congruent

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