Question

In ΔABC, AD is the perpendicular bisector of BC (See adjacent figure). Show that "ABC is an isoscele triangle in which AB = AC.

Answer 1

In the attachment I have answered this problem.

Concept:

Pythagoras theorem:

In a right angle triangle, square on the hypotenuse is equal to sum of the squares on the other two sides.

See the attachment for detailed solution.

Answer 2

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∆.

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

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