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 AB=AC , the bisectors of B and C intersect each other at O. Join A to O. Show that :

  1. OB=OC

  2. AO bisects A

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

Give an Isosceles Triangle ABC

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

Solution:

Given, AB=AC , the bisectors of B and C intersect each other at O

  1. Since ABC is an isosceles with AB=AC,

    B=C 12B=12C (add12bothofside) OBC=OCB (Angle bisectors.) OB=OC (Side opposite to the equal angles are equal.)

  2. In ΔAOB and ΔAOC , AB=AC (Given) AO=AO (Common) OB=OC (Proved above)

    Therefore, ΔAOBΔAOC by SSS congruence condition.

    BAO=CAO (by Corresponding Part of Congruent Triangles)

Thus, AO bisects A.

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

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

Give ΔABC, AD Is the Perpendicular Bisector of BC

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

Solution:

Given, AD is the perpendicular bisector of BC To show, AB=AC

Proof,In ΔADB and ΔADC , AD=AD (Common) ADB=ADC BD=CD (AD is the perpendicular bisector)

Therefore ,ΔADBΔADC (By SAS congruence condition). AB=AC (By Corresponding Parts of Congruent Triangles)

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