Question

in parallelogram ABCD, the angle bisector of angle bisects ab .will angle bisector of angle b will also bisect AD?EXPLAIN.

Answer 1

yes because the opposite angle of parallelogram is same

Answer 2

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.

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