In Fig. 7.8, AD is the bisector of ∠BAC. Prove that AB > BD.

Solution:

Given, 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

✦ Try This: In figure, the sides BC, CA and BA of a ΔABC have been produced to D, E and F respectively. If ∠ACD = 105 and ∠EAF = 45, find all the angles of the ΔABC.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

NCERT Exemplar Class 9 Maths Exercise 7.3 Problem 11

In Fig. 7.8, AD is the bisector of ∠BAC. Prove that AB > BD

Summary:

The (interior) bisector of an angle, also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts. In Fig. 7.8, AD is the bisector of ∠BAC. It is proven that AB > BD

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