SOLUTION: given: triangle ABC is isosceles, CD is the altitude to base AB prove: CD bisects angle ACB i think that we will use the Angle Side Angle postulate?

Algebra ->  Geometry-proofs -> SOLUTION: given: triangle ABC is isosceles, CD is the altitude to base AB prove: CD bisects angle ACB i think that we will use the Angle Side Angle postulate?      Log On


   

Question 474958: given: triangle ABC is isosceles, CD is the altitude to base AB
prove: CD bisects angle ACB
i think that we will use the Angle Side Angle postulate?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


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