Prove that the median from the vertex of an isosceles triangle is the bisector of the vertical angle - Maths - Triangles

Question

Prove that the median from the vertex of an isosceles triangle
is the bisector of the vertical angle

Ankush Jain · Accepted Answer

Consider an isosceles triangle ABC having AD as the median and AB = AC.

Given AD is the median.

⇒ BD = DC

In Δ ABD and Δ ADC, we have

AB = AC

BD = DC

and AD = AD

Therefore, Δ ABD $≅$ Δ ADC [SSS property]

⇒ ∠1 = ∠2 [cpct]

Hence, the median from the vertex of an isosceles triangle is the bisector of the vertical angle.

Prove that the median from the vertex of an isosceles triangle is the bisector of the vertical angle.