Question

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

Answer 1

Heya...!!


continuation ..

from equations 1 ,2 ,3

AB= PQ

BC=QR

AC=PR

By SSS congruence rule

two triangles are congruent

# Hope it helps #

Answer 2

Given that: ΔABC is similar to ΔPQR.
 
And, ar ΔABC =ar ΔPQR

To Prove: ΔABC is congruent to ΔPQR

Proof:

Since, ΔABC is similar to ΔPQR

AB/ PQ = BC/ QR = CA/ PR  


Now, ar ΔABC =ar ΔPQR. 

Therefore ΔABC / ar ΔPQR = 1

We know that for two similar triangles the ratio of their areas is equal to the ratio of square of their corresponding sides

⇒ AB²/PQ² = BC²/QR² = CA²/PR² = 1

⇒ AB= PQ , BC= QR & CA= PR

Thus, by SSS Congruency criteria, ΔABC is congruent to ΔPQR