Question

in a parallelogram ABCD the bisector of angle A also bisects BC at X find a b

Answer 1

   L
 Let the bisector of ∠A bisects the side BC at X.
Given, ABCD is a parallelogram.
∴ AD||BC (Opposite sides of the parallelogram are parallel)
Now, AD||BC and  AX is the transversal  ,
∴ ∠2 = ∠3 (Alternate angles)  ............(1)
and ∠1 = ∠2 (AX is the bisector of ∠A) ................(2)
From (1) and (2), we obtain
∠1 = ∠3
Now, in ΔABX,
∠1 = ∠3
⇒ AB = BX  ( If two angles of a triangle are equal, then sides opposite to them are equal)
⇒ 2AB = 2BX = BX + BX = BX + XC  ( X is the mid point of BC)
⇒ 2AB = BC
⇒ 2AB = AD (Opposite sides of a parallelogram are equal)
∴ AD = 2AB.

Answer 2

Answer:

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