Question

Show that diagonals of a rectangle are equal.

Answer 1

Given that:$\mathrm{ABCD}$ be a rectangle$\mathrm{AC}$and $\mathrm{BD}$are the diagonals.

To prove: Diagonals of rectangle are equal.

Proof:

In $\mathrm{\Delta ABC}$and$\mathrm{\Delta ABD}$, we have

$\mathrm{AB}=\mathrm{AB}$ (common side)

$\angle \mathrm{A}=\angle \mathrm{B}={90}^0$( all angles of rectangles are right angles)

$\mathrm{AD}=\mathrm{BC}$ (opposite sides of rectangle are equal)

By $\mathrm{SAS}$ criteria, $\mathrm{AC}=\mathrm{BD}$.

Thus, diagonals of rectangle are equal. Hence proved.