In a parallelogram ABCD, the bisector of ∠ A also bisects BC at X. Find AB : AD.

Question

In a parallelogram ABCD, the bisector of &#x2220; A also bisects BC at X. Find AB : AD.

Philoid · Accepted Answer

Given,

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,

=