Question

In ∆ABC, a line XY parallel to BC cuts AB at X and AC at Y. If BY bisects ∠XYC, then

 

Options

•  BC = CY

• BC = BY

•  BC ≠ CY

• BC ≠ BY

Answer 1

Given: XY||BC and BY is bisector of

\[\angle\] XYC

Since XY||BC

So

\[\angle\] YBC = \[\angle\] BYC     (Alternate angles)

Now, in triangle BYC two angles are equal. Therefore, the two corresponding sides will be equal.

Hence, BC = CY

Hence option (a) is correct.