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Math Help - Help with basic Geometry proof

  1. #1
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    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

    Thanks in advance for your help!
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  2. #2
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    Quote Originally Posted by juliannec View Post
    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
    ...
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  3. #3
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    Thank you so much for your help, skeeter!
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