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


Answer :

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

figure

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

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