Question

The diagonals of a rectangle are equal.

• A. True
• B. False

Answer 1

The correct option is A

True

The diagonals of a rectangle are equal.
Proof - $ABCD$ is a rectangle with $AC$ and $BD$ as its diagonals.
$ABCD$ is a rectangle
_{$\therefore$ $\angle$ $A$ = ${90}^{\circ }$}
$AD=BC$
$AD$$\parallel$$BC$ and $AB$ is a transversal
_{$\therefore$ $\angle$ $A$ + $\angle$ $B$ = ${180}^{\circ }$
$\Rightarrow$ $\angle$ $B$ = ${90}^{\circ }$}
In
$△$$ABD$ and $△$$BAC$
$AB=BA$
_{$\angle$ $A$ = $\angle$ $B$}
$AD=BC$
_$\therefore$ $△$$ABD$ $\cong$$△$$BAC$
_{$\Rightarrow$ $BD=AC$} (c.p.c.t)
Hence, the diagonals of a rectangle are equal.