Question

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

Answer 1

Answer:

Given: 

ΔABC ~ ΔPQR

ar ΔABC = ar ΔPQR

To Prove: ΔABC ≅ ΔPQR

Proof:

ar ΔABC / ar ΔPQR = 1

AB²/PQ² = BC²/QR² = CA²/PR² = 1

AB = PQ, BC = QR and CA = PR

Therefore, ΔABC ≅ ΔPQR (By SSS criterion of congruence)

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Answer 2

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Answer:

Given: ΔABC ~ ΔPQR

ar ΔABC = ar ΔPQR

To Prove: ΔABC ≅ ΔPQR

Proof:

ar ΔABC / ar ΔPQR = 1

AB²/PQ² = BC²/QR² = CA²/PR² = 1

AB = PQ, BC = QR and CA = PR

Therefore, ΔABC ≅ ΔPQR (By SSS criterion of congruence)

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