Question

prove that if two triangles are similar then they are Congruent.

Answer 1

= taje two tri.
tri.ABC tri.PQR
ab=pq
bc=qr
ac=qr
hence they became congruent

Answer 2

Answer:

Given: ΔABC ~ ΔPQR. &

ar ΔABC =ar ΔPQR

To Prove: ΔABC ≅ ΔPQR

Proof: Since, ΔABC ~ ΔPQR

ar ΔABC =ar ΔPQR. (given)

ΔABC / ar ΔPQR = 1

⇒ AB²/PQ² = BC²/QR² = CA²/PR² = 1

[ USING THEOREM OF AREA OF SIMILAR TRIANGLES]

⇒ AB= PQ , BC= QR & CA= PR

Thus, ΔABC ≅ ΔPQR

[BY SSS criterion of congruence]