Question

In the given figure, the point $P$ bisects $AB$ and $DC$. Prove that
$△APC\cong △BPD$

Answer 1

In given figure P bisect AB and DC

Then P is the mid point of AB and CD

Then $AP=PB$

And $CP=PD$

Then in $\Delta APC$ and $\Delta BPD$

$AP=PB$

$CP=PD$

$\angle APC=\angle BPD$............(vertically opposite angles)

$\therefore \Delta APC\cong \Delta BPD$