Question

Prove that the diagonal of a square divides it into two congruent triangle.

Answer 1

Let $ABCD$ be the square and line $AC$ be its diagonal. We know, in a square all sides are equal and all the angles are right angled.

So, in $ABC$ and $ACD$,

$AB=CD$

angle $ABC=$ angle $ACD$

$AD=BC$

So, by SAS congurency both the triangles are equal.