SSS congruence condition
Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other
Q1 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
Q2 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)