Question

ABCD is a prallelogram. Bisector of angle A also bisect BC at X. Prove that AD=2AB

Answer 1

AB || BC ( ABCD is a parallelogram ) (take the point intersecting BC be X)

the bisector from A is a transversal , therefore ,

Angle 1 = angle 3 ( adjacent angle )

also angle 1 = angle 2 ( the line is a bisector)

therefore angle 2 = angle 3

and AB = BX ( sides opp. to equal angles are equal )

also 2BX = BC ( given)

Therefore 2AB = BC

and BC = AD ( opp sides of a parallelogram are equal )

therefore 2AB = Ad