Q21 of 32 Page 6

If the areas of two similar triangles are equal, prove that they are congruent. (CBSE 2010)




Let us consider two similar triangles as ΔABC ΔPQR (Given)

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. 

If two similar triangles have a scale factor of a : b, then the ratio of their areas is a2 : b2.



Given that,

ar(Δ ABC) = ar(Δ PQR)

Therefore putting in equation (i) we get,

AB = PQ


BC = QR


And,


AC = PR


Hence,


ΔABC ΔPQR (By SSS rule)

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