Question

1. In the given figure, AB|| CD and O is the
midpoint of AD.
Show that (i) AOB = ADOC.
(ii) O is the midpoint of BC.​

Answer 1

Step-by-step explanation:

Given :- AB || CD

O is the mid point of AD

therefore , OA = OD -------- (1)

T.P :- (i) AOB congruent to DOC

(ii) O is also the mid point of OC i.e ; OB=OC

Proof :- AB || CD

ABO = DCO ( Alt angles ) ------ (2)

Also , AOB = DOC ( VOA ) -------- (3)

In AOB and DOC ,

ABO = DCO ( From (2) )

AOB = DOC ( From (3) )

OA = OD ( From (1) )

therefore , AOB congruent to DOC ( by AAS )

So , OB = OC

HENCE PROVED

Hope it will help you .