Question

In ΔABC and ΔPQR, AB = PQ and AC = PR. Which angle of ΔABC should be equal to ΔPQR, so that the two triangles are congruent. Give reason.

Answer 1

Given:

• In ΔABC and ΔPQR, AB = PQ and AC = PR.

Step-wise calculation / Reasoning:

1. AB and AC are the two sides of ΔABC that meet at vertex A; PQ and PR are the two corresponding sides of ΔPQR that meet at vertex P.
2. For the Side–Angle–Side (SAS) congruence criterion, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
3. Therefore, the required angle is the included angle between the equal sides, i.e., ∠A in ΔABC must equal ∠P in ΔPQR. With AB = PQ, AC = PR and ∠A = ∠P, the triangles are congruent by SAS.

∠A should be equal to ∠P.

Hence, ΔABC ≅ ΔPQR by SAS congruence.