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Question
In the following figure, AD is the bisector of ∠BAC. Prove that AB > BD.
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Solution
Given: ABC is a triangle such that AD is the bisector of ∠BAC.
To prove: AB > BD.
Proof: Since, AD is the bisector of ∠BAC.
But ∠BAD = CAD ...(i)
∴ ∠ADB > ∠CAD ...[Exterior angle of a triangle is greater than each of the opposite interior angle]
∴ ∠ADB > ∠BAD ...[From equation (i)]
AB > BD ...[Side opposite to greater angle is longer]
Hence proved.
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