Answer :

Given: The correspondence ∆ABC↔∆PQR is a similarity and AB ≅ PQ.

To prove: ∆ABC and ∆PQR are congruent.

Proof:

The correspondence ∆ABC↔∆PQR is a similarity.

Further, AB ≅ PQ

AB = PQ

AB = PQ, BC = QR, AC = PR

AB ≅ PQ, BC ≅ QR, AC ≅ PR

The correspondence ∆ABC↔∆PQR is a congruence by SSS theorem of congruence.

Hence, ∆ABC and ∆PQR are congruent.

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