# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.1 – Part 3

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Angle Angle Side congruence condition

Q-5. Line l is the bisector of an angle and B is any point on l. BP and BQ are perpendiculars from B to the arms of (see Fig). Show that:

or B is equidistant from the arms of

Solution:

Give, l is the bisector of an angle

BP and BQ are perpendiculars.

In and

(Right angles)

(l is bisector)

(Common line)

Therefore, (by Angle-Angle-Side congruence condition).

by Corresponding Part of Congruent Triangles.

Therefore, B is equidistant from the arms of .

Q-6 In the Figure. , . Show that

Solution:

Given,

To show,

Proof,

(Adding ∠DAC both sides)

In and

(Given)

(Given)

Therefore, (by Side-Angle-Side congruence condition).

(By Corresponding Part of Congruent Triangles)