Question

$AD$ and $BC$ are equal perpendicular to a line segment $AB$. Show that $CD$ bisects $AB$.

Answer 1

Based on the $△AOD$ and $△BOC$

From the figure, we know that $\angle AOD$ and $\angle BOC$ are vertically opposite angles.

So we get

$\angle AOD=\angle BOC$

We also know that

$\angle DAO=\angle CBO={90}^{\circ }$

It is given that $AD=BC$

Therefore, by $AAS$ congruence criterion we get

$△AOD\cong △BOC$

So we get $AO=BO(c.p.c.t)$

Therefore, it is proved that $CD$ bisects $AB$.