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