Question

abcd is a parallelogram. if E is mid point of bc and ae is the bisector of angle A then prove AB=1/2 AD

Answer 1

since AE is the bisector of angle A
Therefore 
angle 1 = 1/2 angle A ..... (1)
since ABCD is a parallelogram is parallelogram
Therefore , AD || BC and AB intersects them.
=> angle A + angle B = 180 ( sum of interior angles is 180)
=> angle B = 180 - angle A
In tri ABE , we have
angle 1 + angle 2 + angle B = 180
=> 1/2 angle A + angle 2 + 180- angle A = 180
angle 2 - 1/2 angle A= 0
angle 2 = 1/2 angle A ..... (2)
from (1) and (2)
angle 1 = angle 2
In tri ABE we have 
BE = AB ( sides opposite to equal angles are equal)
2 BE = 2 AB ( multiplying by 2 both sides )
BC = 2 AB ( E is the mid point of BC )
AD = 2AB ( ABCD is a parallelogram therefore AD = BC )
AB= 1/2 AD