Question

Question 11
In the following figure AD is the bisector of $\angle BAC$. Prove that AB > BD.

Answer 1

Given ABC is a triangle such that AD is the bisector of $\angle BAC$.
To prove: AB > BD.
Proof:
$\angle BAD=CAD$ [$\because$ AD is the bisector of $\angle BAC$]
$\angle ADB>\angle CAD$.
[exterior angle of a triangle is greater than each of the opposite interior angles].
$\Rightarrow \angle ADB>\angle BAD$ [from Eq.(i)].
$\Rightarrow AB>BD$ [side opposite to greater angle is longer].