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

Question

Philoid · Accepted Answer

Given: ∆ABC is isosceles triangle where AB = AC and BD = DC

To prove: ∠BAD = ∠DAC

Proof:

In ∆ABD and ∆ADC

AB = AC …given

BD = DC …given

AD = AD … common side

Thus by SSS property of congruence,

∆ABD ≅ ∆ADC

Hence, we know that, corresponding parts of the congruent triangles are equal

∠BAD = ∠DAC