If the areas of two similar triangles are equal,prove that they are co

1.	If the areas of two similar triangles are equal,prove that they are congurent
Answer» Solution:\xa0Given: ΔABC ~ ΔPQR. &\xa0ar ΔABC =ar ΔPQRTo Prove: ΔABC ≅ ΔPQRProof: 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= PRThus, ΔABC ≅ ΔPQR[BY SSS criterion of congruence]\xa0

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