In following figure if AD if the bisector of `angleABC,` then prove that `AB gt BD`

Explanation

Given ABC is a triangle such that AD is the bisector of `angleABC`
To Prove `AB gt BD`
Proof Since ,AD if the bisector of `angleBAC.`
`therefore " "angleBAD =CAD " "….(i)`
`" But " " "angleADB gt angleCAD `
[exterior angle of a triangle is greater than each of the opposite interior angle ]
` therefore " "angleABD gt angle CAD " "["from Eq.(i)"]`
`rArr " " AB gt BD " "["side opposite to greater angle is longer "]`