Q. 103.7( 6 Votes )

Two triangles are similar. Prove that if sides in one pair of corresponding sides are congruent, then the triangles are congruent.

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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