# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 – Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Corresponding Parts of Congruent Triangle (CPCT)

CPCT means that the corresponding sides are equal and the corresponding angles are equal.

Q-1 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.