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

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SSS congruence condition

Give SSS congruence condition it means three side are equal.

Give SSS Congruence Condition

Give SSS congruence condition it means three side are equal.

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 :

  1. AO bisects

an Isosceles Triangle ABC

An isosceles triangle ABC and AB=AC, the bisectors of angle B and angle C intersect each other at O. Join A to O.

Solution:

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

  1. Since ABC is an isosceles with

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

  2. 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 .

Triangle ABC, AD Is the Perpendicular Bisector of BC

Triangle ABC, AD is the perpendicular bisector of BC show Triangle ABC is an isosceles triangle in which AB = AC.

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)