Question

5. Prove :

If the perpendicular from the vertex of a triangle
bisects the base, then prove that the triangle is an
isosceles triangle.​

Answer 1

Answer:

Let ABC be an isosceles triangle such that AB=AC.

Let AD be the bisector of ∠A.

To prove:- BD=DC

Proof:-

In △ABD&△ACD

AB=AC(∵△ABC is an isosceles triangle)

∠BAD=∠CAD(∵AD is the bisector of ∠A)

AD=AD(Common)

By S.A.S.-

△ABD≅△ACD

By corresponding parts of congruent triangles-

⇒BD=DC

Hence proved that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.

Answer 2

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