Given: segment BD bisects angle ABC. prove: segment BD is the altitude

Question

I have an isosceles triangle and I have the given which is segment BD bisects angle ABC. I have to prove segment BD is the altitude. How do I prove that???

Answer 1

ALWAYS begin by making the drawing.

I assume that angle B is the vertex angle of an isosceles triangle.

 

Then triangles ABD and CBD are congruent by SAS, and therefore BD is perpendicular to AC because the two angles at D are equal and supplementary, hence right angles, and that makes BD the altitude of the isosceles triangle.

 

Again, always draw the figure & label it on the way to any proof.