Question 5

Triangle ABC as shown in the figure has line XY parallel to the BC and the line BY is the bisector of angle XYC. Which of the following option is correct?

Solution

$$\because$$ XY is parallel to BC

=> $$\angle$$ XYB = $$\angle$$ YBC -------------(i) [Alternate interior angles]

Also, BY is the angle bisector of $$\angle$$ XYC.

=> $$\angle$$ XYB = $$\angle$$ BYC --------------(ii)

From equations (i) and (ii), we get : $$\angle$$ YBC = $$\angle$$ BYC

$$\therefore$$ BC = YC [Sides opposite to equal angles]

=> Ans - (B)

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