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प्रश्न
AD bisects ∠BAC of ΔABC. Prove that AB > BD.
सिद्धांत
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उत्तर
Given: AD bisects ∠BAC of triangle ABC.
To Prove: AB > BD
ABC is a triangle.
AD is the bisector of ∠BAC.
We have to prove that AB > BD
Since AD is the bisector of ∠BAC
∠BAD = ∠CAD ...(1)
We know that the exterior angle of a triangle is greater than each of the opposite interior angles.
∠ADB > ∠CAD
From (1), ∠ADB > ∠BAD
We know that in a triangle a side opposite to a greater angle is longer.
The side AB is greater than BD.
Therefore, AB > BD
Hence, proved.
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