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In the adjoining figure, bisector of ∠B AC intersects side BC at point D. Prove that AB > BD.

Given: Bisector of ∠BAC intersects side BC at point D. 

To prove: AB > BD

1 Answer

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Best answer

∠BAD ≅ ∠DAC ….(i) [Seg AD bisects ∠BAC] 

∠ADB is the exterior angle of ∆ADC. 

∴ ∠ADB > ∠DAC ….(ii) [Property of exterior angle] 

∴ ∠ADB > ∠BAD ….(iii) [From (i) and (ii)] 

In AABD,

 ∠ADB > ∠BAD [From (iii)] 

∴ AB > BD [Side opposite to greater angle is greater]

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