Question

ABCD is a parallelogram. If the line joining the mid-point of side BC to vertex A bisects angle A, then prove that bisector of angle B also bisects AD.Please Help

Answer 1

In parallelogram ABCD ,

Bisector of ∠A bisects BC at X

∵ AD││BC and AX cuts them so

∠DAX = ∠AXB (alternate angles)

∠DAX = ∠XAB (AX is bisector of ∠A)

∴∠AXB = ∠XAB

AB= BX (sides opposite of equal angles)

Now,AB/AD= BX/BC

=AB/AD=BX/2BX

(since,X is mid point of BC)

=AB/AD=1/2

Hence,

AB:AD=1:2.

FOR MORE DETAILS PLEASE REFER INAGE,

Answer 2

Answer:

Proved in the explanation.