...I've been having a bit of trouble with geometry proofs. I'm really trying to learn and figure this one out myself, but I could use a little guidance. I'm not sure if I'm missing steps or just making a huge mistake without noticing. If someone could look it over and tell me what I should fix/improve, that would be great.
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; CD is the altitude to base AB.
note what you are trying to prove
1. Triangle ABC is isosceles. - Given
2. AC is congruent to BC - definition of isosceles triangle
3. CD is altitude to base AB - given
4. <CDA and <CDB are congruent right angles - definition of altitude
5. CD is congruent to CD - reflexive property
6. Triangle CDA is congruent to triangle CDB - hypotenuse-leg theorem
7. angle ACD is congruent to angle BCD ... cpctc
8. CD bisects the vertex angle ACB ... def. of an angle bisector