How i prove the congruent of two similar triangles are equal of exercise 6.4 of class 10th. Sir please help to solve this problem If the areas of two similar triangles are equal, prove that they are congruent.

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# If the areas of two similar triangles are equal, prove that they are congruent. Q.4

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Say Î”ABC and Î”PQR are two similar triangles and equal in area

Now let us prove Î”ABC â‰… Î”PQR.

Since, Î”ABC ~ Î”PQR

âˆ´ Area of (Î”ABC)/Area of (Î”PQR) = BC

^{2}/QR^{2}â‡’ BC

^{2}/QR^{2}Â =1 [Since, Area(Î”ABC) = (Î”PQR)â‡’ BC

^{2}/QR^{2}â‡’ BC = QR

Similarly, we can prove that

AB = PQ and AC = PR

Thus, Î”ABC â‰… Î”PQR [SSS criterion of congruence]