Question

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

Answer 1

All angles would be same and sides will be proportional to each other.

$\Delta =\sqrt{\left(\frac{a+b+c}{2}\right)\left(\frac{a+b-c}{2}\right)\left(\frac{a-b+c}{2}\right)\left(\frac{b+c-a}{2}\right)}=k^2{\Delta }^{\prime }$

If the areas are equal then $k=1$ then all sides also becomes same which makes bothb the triangles congruent.