Prove Angel Bisector Theorem

1.	Prove Angel Bisector Theorem
Answer» Given:AD bisects angle ATo prove:BD/DC=AB/AC Construction:Extend AB to E such that CE parallel to AD.Proof:angle BAD=angle DAC (given)AD paralel CEangle BAD=angle AEC (corresponding angle)angle DAC=angle AECangleDAC=angleACE(alt.int.angle)angle ACE=angle AECSo,AC=AEIn ∆BECAD parallel CEBD/DC=BA/AE(by bpt)BD/DC=AB/AC(proved)

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