Question

D is a point on side BC of a ∆ABC such that AD bisects ∠BAC. Then ________.

Answer 1

In ∆ABC, AD is the bisector of ∠A.

∴ ∠BAD = ∠CAD .....(1)

We know that exterior angle of a triangle is greater than each of interior opposite angle.

In ∆ABD,

∠ADC > ∠BAD

⇒ ∠ADC > ∠CAD [Using (1)]

In ∆ADC,

∠ADC > ∠CAD

∴ AC > CD (In a triangle, the greater angle has the longer side opposite to it)

Similarly, AB > BD

D is a point on side BC of a ∆ABC such that AD bisects ∠BAC. Then ___AC > CD and AB > BD___.