Question

In triangle ABC a line XY parallel to BC cuts AB at X and AC at Y.If BY bisects angle XYC ,proove that angle CYB = angle CBY?

Answer 1

Here , XY is parallel to BC
Angle BYX = Angle BYC since By is an angle bisector
Therefore, angle YBC = Angle BYX since they form alternate interior angle
Therefore , Angle BYX = CYB

Answer 2

Answer:

Step-by-step explanation:

In ΔABC, A line XY is parallel to BC and  BY bisects ∠XYC which means

∠BYX=∠BYC                                                                                                  (1)

Also, since XY is parallel to BC, then ∠YBC=∠BYX( Alternate angles)     (2)

therefore, from (1) and (2), wehave

∠YBC=∠BYX and ∠BYX=∠BYC  

⇒∠YBC=∠BYC  

Hence proved.