Question 96735
Given : triangle ABC is isosceles
        CD is the altitude to the base of the triangle 
to Prove: Line Segment CD bisects Angle ACB ie  angle ACD = angle BCD

Proof:
   
   In triangles ACD and BCD 
         AC = BC              Sides of an isosceles triangle ABC
         CD = CD              Common side of the two  triangles
        angle ADC = BDC =90   given CD is the altitude to the base

   therefore triangle ACD is Congruent to triangle BCD  ( by the RHS theorem)
  
                                                   right angle-hypotunese-side
 therfore AD=BD 
 and hence angle ACD = angle BCD  angles opposite to the equal sides are also equal