Question

Show that each angle of a rectangle is a right angle.

Answer 1

Let $ABCD$ be a rectangle. Now, we know that every rectangle is also a parallelogram.

Consider $\Delta ADB$ and $\Delta BCD$

$AD=BC$ [Opposite sides are equal]

$AB=AB$ [Common base]

$DB=AC$ [Diagonals of a rectangle are equal]

Therefore $\Delta ADB\cong \Delta BCA$ by SSS rule.

Hence, $\angle DAB=\angle CBA$ [By CPCT]

But adjacent angles of a parallelogram are supplementary.

$\Rightarrow \angle DAB+\angle CBA={180}^{\circ }$

$\Rightarrow 2\angle DAB={180}^{\circ }$

$\therefore \angle DAB=\angle CBA={90}^{\circ }$

Also, opposite sides of a parallelogram are equal, therefore, each angle id of ${90}^{\circ }$ of rectangle $ABCD$.