Question

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

(a) BC = CY
(b) BC = BY
(c) BC ≠ CY
(d) 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.