Math, asked by archana2025, 1 year ago

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

Answers

Answered by kavusingh85
15

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]


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Answered by srimanthbalaji
2

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}

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