Question

In Fig, If AD bisects ∠ A. Prove that AB > BD​

Answer 1

Answer:

By inequalities property

AB is greater side in triangle ABD

that is angle C is greater

AB is opposite to angle C

that is AB > BD

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Answer 2

$\red{\boxed{\huge Answer}}$

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.

So, ∠BAD = CAD …(i)

∴ ∠ADB > ∠CAD [exterior angle of a triangle is greater than each of the opposite interior angle]

∴ ∠ADB > ∠BAD [from Eq. (i)]

AB > BD [side opposite to greater angle is longer]

Hence proved.