Question

if the areas of two similar triangles are equal prove that they are congruent​

Answer 1

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]

pls mark brainliest

Answer 2

Solution==>

Given=>∆ABC~∆PQR, and

ar of ∆ABC~∆PQR

To Prove=>∆ABC and ∆PQR are congurent.

Proof=> ar ΔABC/ar ΔPQR =

AB²/PQ²=BC²=QR²=AC²=PR²

given that area of triangles are equal,

ar ΔABC/ar ΔABC=AB²/PQ²=BC²=QR²=AC²=PR²

1=AB²/PQ² = BC²/QR² = CA²/PR²

AB = PQ, BC = QR and CA = PR

Therefore, ΔABC ≅ ΔPQR (By SSS criterion of congruence