Question

Prove that the diagonals of a rectangle are of equal length.

Answer 1

A rectangle is a parallelogram with opposite sides equal and the measure of each angle is ${90}^{\circ }$

In above rectangle, consider rectangles ABC and DCB.

$\angle ABC=\angle DCB={90}^{\circ }$ [Angles of rectangle]

$BC=BC$ (common side)

$AB=DC$ (Opposite sides of a parallelogram are equal)

Hence, $△ABC\cong △DCB.$

$AC=DB$ [CPCT]

Hence the diagonals of a rectangle are equal.