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