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