Question 474958
<pre>
{{{drawing(600,400,-1.5,1.5,-1.5,1.5, locate(-1,0,A),
locate(1,0,B),locate(0,1.2,C), green(line(0,1,0,0)),
triangle(-1,0,1,0,0,1), locate(0,0,D) )}}}

Triangles ADC and BDC are right triangles (due to
CD being an altitude)

The two acute angles in a right triangle are complementary.

Angles A and B are congruent because they are base angles
of isosceles triangle ABC.

Therefore angles ACD and BCD are congruent because
they are complements of congruent angles A and B.

Therefore, CD bisects angle ACB. 

You can write that up in a two column proof.

Edwin</pre>