Question

In ΔABC and ΔPQR, ∠A = ∠R and ∠B = ∠P. Which side of ΔABC should be equal to ΔPQR, so that the two triangles are congruent. Give reason.

Answer 1

Given:

• In ΔABC and ΔPQR, ∠A = ∠R and ∠B = ∠P.

Step-wise calculation:

1. From the two angle equalities we get the correspondence of vertices: A ↔ R, B ↔ P, C ↔ Q.
2. The side included between ∠A and ∠B is AB; the corresponding side included between ∠R and ∠P is RP (PR).
3. If AB = PR, then the two triangles have two angles and the included side equal, hence they are congruent by the ASA criterion.

As an alternative, if a corresponding non‑included side is equal, e.g., BC = PQ, the triangles would be congruent by AAS.

AB must be equal to PR.

Therefore, ΔABC ≅ ΔPQR by ASA.