Question

AD is an altitude of an isosceles triangle ABC in which AB=AC.Show that,1)AB bisects BC 2)AD bisects angle A

Answer 1

Construct the figure. There'll be two triangles namely ▲ABD and ▲ACD.

Now, In those two triangles:

AB = AC (Given)

∠ADB = ∠ADC (Each equal bcoz of altitude)

and, AD=AD (Common)

Hence these two triangles are congruent by RHS Criterion.

Now:

1: BD = CD (C.P.C.T)

and 2: ∠BAD=∠CAD (C.P.C.T)

Answer 2

CRM

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