Question

If the area of two similar triangle are equle , 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

Answer:

Step-by-step explanation:

GIVEN AREA OF TWO SIMILAR TRIANGLE ARE EQUAL

LET THE TWO TRIANGLES BE TRI ABC AND TRI PQR

GIVEN T ABC SIMILAR T PQR

WE KNOW THAT

AREA T ABC / AREA T PQR = ( AB/PQ)2 = ( BC/QR) 2 = (AC/PR)2

1ST CASE - WHEN A( ABC / A( PQR) = ( AB/PQ)2

BUT A ABC = A PQR

SP

1 = ( AB / PQ ) 2

AB sqr = PQ sqr

take root both sides

we get

AB = PQ

SIMILARLY WE GET

BC = QR AND AC=PR BY EQUATING

WE PROVED THAT ALL THREE SIDES ARE EQUAL

HENCE THEY ARE CONGRUENT BY SSS CONGRUENCY

PLS MARK AS BRAINLEST AND THANKS!