Prove that the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Question

This is a two column proof

Given: ∆ABC is an isosceles triangle. Line BD bisects ∠B

Prove: line BD is the perpendicular bisector of line AC

Answer 1

Draw and label of a diagram!

You provide the reasons

 

ΔABC is isosceles

m∠A = m∠B

∠A ≅ ∠B

AB = CB

AB ≅ CB

m∠ABD = m∠CBD

∠ABD ≅ ∠CBD

ΔABD ≅ ΔCBD