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

Say $$\triangle$$ ABC and $$\triangle$$ PQR are two similar triangles and equal in area

Now let us prove $$\triangle$$ ABC $${\displaystyle \cong }$$ $$\triangle$$ PQR.

Since, $$\triangle$$ ABC ~ $$\triangle$$ PQR
$$\frac{Area of ( \triangle ABC)}{Area of (\triangle PQR)}$$ = $$\frac{BC^2}{QR^2}$$
$$\frac{BC^2}{QR^2}$$ = 1
[Since, Area($$\triangle$$ ABC) = ($$\triangle$$ PQR)
$$BC^2=QR^2$$
BC = QR

Similarly, we can prove that
AB = PQ and AC = PR