NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.1 – Part 3
Angle Angle Side congruence condition
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 AngleAngleSide congruence condition).

by Corresponding Part of Congruent Triangles.
Therefore, B is equidistant from the arms of .
Q6 In the Figure. , . Show that
Solution:
Given,
To show,
Proof,
(Adding ∠DAC both sides)
In and
(Given)
(Given)
Therefore, (by SideAngleSide congruence condition).
(By Corresponding Part of Congruent Triangles)