Question

Line segment AB is parallel to another equal line segment CD. O is the mid point of
AD. Prove that (i) AAOB = ADOC (ii) O is also the mid point of BC.​

Answer 1

Answer:

Explanation:

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.