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?

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(20059) (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

RELATED QUESTIONS
PROVE: If an isosceles triangle has an altitude from the vertex to the base, then the... (answered by vleith,gonzo)

(given) triangle ABC is isosceles; line CD is the altitude to base line AB (to proove)... (answered by ilana)

PROVE: If an isosceles triangle has an altitude from the vertex to the base, then the... (answered by solver91311)

I am stuck on this proof. It is: Prove: If an Isosceles triangle has an altitude from... (answered by stanbon)

GIVEN: TRIANGLE ABC IS ISOSCELES; LINE SEGMENT CD IS THE ALTITUDE TO BASE OF LINE SEGMENT (answered by mathslover)

Given: Triangle ABC is isosceles and segment CD bisects angle ACB. Prove; D is the... (answered by ikleyn)

Prove: If an isosceles triangle has an altitude from the vertex to the base, then the... (answered by venugopalramana)

Prove: If an isosceles triangle has an altitude from the vertex to the base, then the... (answered by Edwin McCravy)

Hi All, I'm a HS Senior with my last class in Geometry, I saw a problem similar to mine, (answered by jim_thompson5910,stanbon)