SOLUTION: I am stuck on this proof. It is: Prove: If an Isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle. Given: Triangle ABC is

Algebra ->  Geometry-proofs -> SOLUTION: I am stuck on this proof. It is: Prove: If an Isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle. Given: Triangle ABC is       Log On


   

Question 33432: I am stuck on this proof. It is:
Prove: If an Isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.
Given: Triangle ABC is isosceles; Segment CD is teh altitude to base Segment AB.
To prove:Segment CD bisects Angle ACB
This is a problem our teacher gave us to do and i don't understand how to write proofs and i was wondering if you could help me. Thank you
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Need to prove angle ACD= angle BCD
angle CDA is a right angle because of definition of altitude
angle BDA is a right angle because of definition of altitude
Therefore angle CDA= angle BDA
angle A = angle B because they are opposite equal sides of a isos. triangle
Therefore angle ACD = angle BCD because the other corresponding angles are equal.
Cheers,
Stan H.