Question

in the figure if angle BAO = angle DCO and OC =OD,show that AB||CD.

Answer 1

angle bao=angle dco...............1
oc=od
therefore angle ocd =odc............2
fm 1 and 2
angle bao=angle cdo...axiom 1
so angle bao cdo are alternate angles hence ab is
parallel to cd

Answer 2

We know that angle BAO= angle DCO (1)
and, OC=OD
so, angle COD= angle DCO (because angles opposite to equal sides are always equal to each other)
In (1): We can write angle CDO in the place of angle DCO because they both are equal then we will get: angle BAO= angle CDO
These angles are alternate interior angles on the lines AB and CD and are equal so we can say that AB||CD.