Question

$AN$ & $CP$ are perpendicular to the diagonal $BD$ of a parallelogram $ABCD$. Prove that :
(i) $△ADN=△CBP$
(ii) $AN=CP$

Answer 1

Solution:

In $△ADN$ and $△CBP$

$AD=CB$ (opposite side of parallelogram)

$\angle AND=\angle CPB$ (each ${90}^{\circ }$)

$\angle ADN=\angle PBC$ ($AD\parallel BC,BD$ is transversal) (alternate interior angles)

1. Therefore,$△ADN$=$△CBP$ (ASA rule)

2. $AN=CP$ (By cpct)

Hence proved.