Question

10. In a parallelogram ABCD, the angle bisector of A bisects BC. Will angle bisector of B also bisects AD? Give reason.​

Answer 1

ABCD is a parallelogram. Mid-point of BC is E

✧ Join A to E, ∠EAD = ∠EAB ----- (1)

AD is parallel to BC and AE is a transversal.

∠EAD =∠BEA ----- (2) [Alternate angle] .

✧ ∠EAB = ∠BEA [From (1) and (2)]

AB = BE --(3)

✧ But BE = BC/2 = AD / 2 ------(4)

✧ Put value of BE in equation (3)

AB = 1/2 AD [Proved]