Question

Two lines AB and CD interest at O such tht BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

Answer 1

Given : Two lines AB and CD intersed each other at O such that AD = BC and AD || BC

To prove : AB and CD bisect each other i.e. AO = OB and CO = OD

Proof : In $\Delta AODand\Delta BOC,$

$AD=BC\left(Given\right)\angle A=\angle B\left(Alternateangles\right)\angle D=\angle C\left(Alternateangles\right)\therefore \Delta AOD\cong \Delta BOC\left(ASAaxiom\right)\therefore AO=OBandAO=OC(c.p.c.t.)$

Hence AB and CD bisect each other