Question

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

Answer 1

It is proven that the diagonals of a rectangle divide it in two congruent triangles.

How is it so?

Here, ABCD is a rectangle.

AC is diagonal of a rectangle.

In △ABC and △CAD

⇒ AB = DC [ Opposite sides of rectangle ]

⇒ BC = AD [ Opposite sides of rectangle ]

⇒ AC = CA [ Common side ]

∴ △ABC ≅ △CAD [ By SSS congruence property ]