Question 339653
{{{drawing(400,400,-1.5,1.5,-.5,2.5, triangle(-1,0,0,0,0,2),triangle(1,0,0,0,0,2),
locate(-1,0,A), locate(0,0,D), locate(1,0,B), locate(0,2.1,C),
rectangle(0,0,.1,.1) 
)}}}
<pre>
Plan:

The measures of AC and BC are equal because they are legs of isosceles triangle ABC.

Angles ADC and BDC are right angles because CD is an altitude, which is
perpendicular to the base.

The measure of CD is equal to itself.

Right triangles ADC and BDC are congruent because two right triangles are
congruent if the measures of the hypotenuse and a leg of one right triangle
are equal to the measures of the corresponding parts of the other right
triangle.

Angle ACD and Angle BCD have equal measures because they are corresponding
parts of congruent right triangles ADC and BDC.

CD bisects angle ACB because it divides the angle ACB into two angles with
equal measures, ACD and BCD. 

Now you can write the two-column proof.

Edwin</pre>