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Question

In the alongside diagram, ABCD is parallelogram. Prove that : AB=2BC
194916_70daeebffbb44ef6a97e7d5d437cae3e.png

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Solution

Given, ABCD is a parallelogram
The bisectors of A, bisect DC at E
AB||CD [opposite sides of a parallelogram are equal]
AB||CD and AE is transversal
BAE=AED [alternate angle]....(i)
$\angle DAE =\angle BAE [AE is the bisector of \angle A]....(ii)
From (i) and (ii),
AED=DAE
in DAE
AED=DAE
AD=DE [If two angles of a triangle are equal, then sides opposite to them are equal.]
2AD=2DE=DE+DE=DE+EC
2AD=DC
AD=BC and DC=ABAB=2BC


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