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Linear Pair

In ABC, a lin...

Question

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

A

BC = CY

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B

BC = BY

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C

BC CY

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D

BC = XY

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Solution

The correct option is A BC = CY
As $X Y | | B C$
$∠ X Y B = ∠ C B Y - (1)$ (..... Alternate interior angles)

Sinc $B Y$ bisects $∠ X Y C$

$⟹ ∠ X Y B = ∠ C Y B$

eqs.(1) $⟹ ∠ C B Y = ∠ C Y B$
$B C = C Y$ ( side opposite to equal angles are equal)

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