Question

Prove that the bisector of the top angle
of an isosceles triangle bisects the base
at right angles.

Answer 1

Answer:

Given : In the figure attached,

Triangle ABC is an isosceles triangle.

AB = AC

AD is the angle bisector of ∠BAC.

∠BAD ≅ ∠CAD

To Prove : BD ≅ CD and ∠ADB ≅ ∠ADC ≅ 90°

Proof : From the ΔABD and ΔACD,

AB ≅ AC [Given]

AD is common in both the triangles.

∠BAD ≅ ∠CAD [Given]

By the property of (SAS) of congruence both the triangles ΔABD and ΔACD will be congruent.

Therefore, ∠ADB ≅ ∠ADC ≅ \frac{180}{2}=90

2

180

=90 degrees

and BD ≅ CD

Hence proved.