NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 – Part 1
Corresponding Parts of Congruent Triangle(CPCT)
CPCT means that the corresponding sides are equal and the corresponding angles are equal.
Q1 and are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig). If AD is extended to intersect BC at P, show that



AP bisects as well as

AP is the perpendicular bisector of BC.
Solution:
Given, and are two isosceles triangles.

In (Common line) ( is isosceles) ( is isosceles)
Therefore, by SSS congruence condition

In (Common line) ( so by CPCT) (is isosceles)Therefore, by SAS congruence condition.

by Corresponding Parts of Congruent Triangles as .AP bisects . ……………..equation (1)
also,In and , (Common line) ( is isosceles.) ( so by Corresponding Parts of Congruent Triangle(CPCT)).
Therefore, by SSS congruence condition.
Thus, by CPCT. ………….equation(2)By (1) and (2) we can say that AP bisects as well as .

(by CPCT as )and ……………equation(3) also, (BC is a straight line.) ……………equation(3)
From (1) and (2),
AP is the perpendicular bisector of BC.