Question

"Question 2 In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.

Class 9 - Math - Triangles Page 123"

Answer 1

Congruence of triangles:
Two ∆’s are congruent if sides and angles of a triangle are equal to the corresponding sides and angles of the other ∆.

In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.

It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.

Criteria for congruence of triangles:
There are 4 criteria for congruence of triangles.

SAS( side angle side):
Two Triangles are congruent if two sides and the included angle of a triangle are equal to the two sides and included angle of the the other triangle.

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Given:
AD is the perpendicular bisector of BC.

To Prove:
∆ABC is an isosceles ∆.
i.e, AB = AC

Proof:
In ΔADB & ΔADC,
AD = AD (Common)
∠ADB = ∠ADC . ( each 90°)

BD = CD (AD is the perpendicular bisector)

Therefore, ΔADB ≅ ΔADC
( by SAS congruence rule)

AB = AC (by CPCT)
So, ∆ABC is an isosceles∆.


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Hope this will help you....