# Thread: Help with basic Geometry proof

1. ## Help with basic Geometry proof

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.

Proof:

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

2. Originally Posted by juliannec
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

Proof:

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
...

3. Thank you so much for your help, skeeter!