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

Here AB and QR are included between equal angles.

Side of ∆ PQR is QR that should be equal to side AB of ∆ ABC

From the 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 ≅ ∆ EDF

Therefore, the side QR of ∆ PQR should be equal to side AB 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 DE 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 1

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆ PQR should be equal to side AB 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. The side QR of ∆ PQR should be equal to side AB of ∆ ABC so that the two triangles are congruent

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