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.
Plan: (I'm not sure if this is detailed enough? I'm only given one line to write on, so I don't think they expect a full paragraph proof.) Prove that triangle CAD is congruent to triangle CDB, then that point D is the midpoint of AB.
1. Triangle ABC is isosceles. - Given
2. AB is congruent to CB - definition of isosceles triangle
3. CD is altitude to base AB - given
4. <CA 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. AD is congruent to DB - corresponding parts of congruent angles are congruent
8. D is the midpoint of AB - midpoint theorem
9. CD bisects <ACB - perpendicular bisector theorem
Thanks in advance for your help!