If areas of two similar triangles are equal, thenprove that the triang

1.	If areas of two similar triangles are equal, thenprove that the triangles are congruent.
Answer» Given: ΔABC ~ ΔPQR. & ar ΔABC =ar ΔPQR To Prove: ΔABC ≅ ΔPQR Proof: Since, ΔABC ~ ΔPQRar 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]

If areas of two similar triangles are equal, thenprove that the triangles are congruent.

Answer»

Given: ΔABC ~ ΔPQR. &

ar ΔABC =ar ΔPQR

To Prove: ΔABC ≅ ΔPQR

Proof: Since, ΔABC ~ ΔPQRar 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]