Question

line segment AB is a parallel to another line segment CD. O is the mid point of AD. show that O is also the midpoint of BC.
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Answer 1

Answer:

(diagram attached)

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.

Answer 2

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Hope it helps....!!