Question

In the given figure, AB and CD are
perpendicular to the line segment AD. AD and BC
intersect at P such that PA = PD. Prove that:
(1) AB = CD
(ii) P is the mid-point of BC.
​

Answer 1

Answer:

Given: AB is parallel to another line segment CD.

O is the midpoint OF AD

In ΔAOB and ΔDOC

∠AOB=∠COD ...(Vertically opposite angle )

∠BAO=∠CDO ...(Given AB parallel to DC and AD meet both lines so alternate angles are equal)

AO=OD ....(O is the midpoint of AD )

ΔAOB≅ΔDOC ...ASA test

So, BO=CO

Then, O is the midpoint of BC.