# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 – Part 1

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SSS congruence condition

Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other

Q-1 In an isosceles triangle ABC, with , the bisectors of and intersect each other at O. Join A to O. Show that :

AO bisects

Solution:

Given,, the bisectors of and intersect each other at O

Since ABC is an isosceles with

(Angle bisectors.) (Side opposite to the equal angles are equal.)

In and , (Given) (Common) (Proved above)

Therefore, by SSS congruence condition.

(by Corresponding Part of Congruent Triangles)

Thus, AO bisects

Q-2 In ΔABC, AD is the perpendicular bisector of BC (see Fig). Show that ΔABC is an isosceles triangle in which .

Solution:

Given, AD is the perpendicular bisector of BC To show,

Proof,In and , (Common) (AD is the perpendicular bisector)

Therefore (By SAS congruence condition). (By Corresponding Parts of Congruent Triangles)