Question

Iff areas of two sim triangles are equal,then prove that they are congruent.​

Answer 1

Answer:

Step-by-step explanation:

Use the theorem that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides , then prove that they are congruent.

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Solution:

[Fig is in the attachment]

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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Hope this will help you.

Answer 2

[HeY Mate]

Answer:

Question:

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

Solution:

Let ΔABC and ΔPQR be the two similar triangles with equal area.

To Prove: ΔABC ≅ ΔPQR.

Proof:

ΔABC ~ ΔPQR

∴ Area of (ΔABC)/Area of (ΔPQR) = BC2/QR2

⇒ BC2/QR2 =1 [Since, ar (ΔABC) = ar (ΔPQR)]

⇒ BC2/QR2

⇒ BC = QR

Similarly, we can prove that

AB = PQ and AC = PR

Therefore, ΔABC ≅ ΔPQR [SSS criterion of congruence]

I Hope It Helps You✌️