Question

If ΔABC ≅ ΔPQR, is it true to say that AB = PR? Why?

Answer 1

Given: ΔABC ≅ ΔPQR

Step-wise calculation:

1. The vertex order in the congruence statement gives the correspondence A ↔ P, B ↔ Q, C ↔ R.

2. Corresponding sides therefore are AB ↔ PQ, BC ↔ QR, CA ↔ RP.

3. By the Corresponding Parts of Congruent Triangles are Congruent (CPCT) principle, corresponding sides are equal, so AB = PQ, BC = QR and CA = RP.

4. PR is the side joining P and R, which corresponds to CA (not AB) under the given correspondence.

No - AB = PR is not necessarily true.

From ΔABC ≅ ΔPQR we get AB = PQ not AB = PR.

AB = PR would only hold if the triangles were written with a different correspondence that pairs AB with PR for example if the congruence were ΔABC ≅ ΔPRQ so that B ↔ R.