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 Equation , the bisectors of Equation and Equation intersect each other at O. Join A to O. Show that :

  1. Equation

  2. AO bisects Equation

Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [A, C] Segment h Segment h: Segment [C, B] Segment i Segment i: Segment [D, C] Segment j Segment j: Segment [D, A] Segment k Segment k: Segment [D, B] A text1 = "A" B text2 = "B" C text3 = "C" O text4 = "O"

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

  1. Since ABC is an isosceles with Equation

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

  2. In Equation and Equation , Equation (Given) Equation (Common) Equation (Proved above)

    Therefore, Equation by SSS congruence condition.

    Equation (by Corresponding Part of Congruent Triangles)

Thus, AO bisects Equation

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

Angle α Angle α: Angle between C_1, D, A Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [B, C_1] Segment h Segment h: Segment [C_1, A] Segment i Segment i: Segment [C_1, D] A text1 = "A" C text2 = "C" D text3 = "D" B text4 = "B"

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, Equation

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

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

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