ABCD IS A PARALEELOGRAM AND ANGLE DAB =60 . IF THE BISECTORS AP AND BP OF ANGLES A AND B RESPECTIVELY MEET AT P ON CD . PROVE THAT P IS MID PT OF CD

Dear student,

PAB= PAD= 30° ….as AP is bisector

APD = 30°…..as AB ll CD

In triangle APD,

AD=DP………(i) ….sides opposite to equal angles

Similarly, in triangle PBC

PBC = BPC= 60°

BC=PC…..(ii) ..sides opposite to equal angles

CP=PD….from (i) and (ii) as AD=BC being opp sides of a parallelogram

Thus, P is the mid point of CD.

We hope that clarifies your query.

Regards,

Team

TopperLearning