Question

Prove that the diagonals of a rectangle divide it in two congruent triangles.

Answer 1

Here, $ABCD$ is a rectangle.

$AC$ is diagonal of a rectangle.

In $△ABC$ and $△CAD$

$\Rightarrow$ $AB=DC$ [ Opposite sides of rectangle ]

$\Rightarrow$ $BC=AD$ [ Opposite sides of rectangle ]

$\Rightarrow$ $AC=CA$ [ Common side ]

$\therefore$ $△ABC\cong △CAD$ [ By $SSS$ congruence property ]