Question

Prove that the bisectors of the interior angles of a rectangle form a rectangle.

Answer 1

$\angle 1=\frac{90}{2}={45}^o$

Similarly, $\angle 2=\frac{90}{2}={45}^o$

In $△AXD$,

$=180-45-45={90}^o$

$\angle WXY={90}^o$ [vertically opposite angles]

Similarly in $△BCZ$,

$\angle CZB=\angle WZY={90}^o$

Since all the angles will be ${90}^o$ and hence it will be a rectangle.