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Math Help - Need help, 3 problems to graduation!!! please help!!

  1. #1
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    Exclamation Need help, 3 problems to graduation!!! please help!!

    Hi All, I'm a student of The American school and the only thing I have between me and my diploma is 3 proofs. I've gotten help from several people but we can't seem to figure out these proofs. Any help would be awesome!!


    Given: In triangle ABC, (angle) B = 120 degrees

    Prove: Angle A is not equal to 60 degrees

    Plan: Use an indirect proof.

    NOTE: Write the proof using the paragraph method.









    Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogram is a rhombus. (State your plan and give a proof.)

    Given: ABCD is a parallelogram with (angle) 1 congruent with (angle) 2

    To Prove: ABCD is a rhombus

    Plan
    :


    Thanks to Soroban for help with this proof =)




    Prove that the tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a two-column proof.




    Thanks so much to anyone who can help me with one or all of these proofs. I'm so ready to be finished with High School LOL
    Last edited by proofsRkickingmybutt; February 3rd 2009 at 05:53 PM.
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  2. #2
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    Hello, proofsRkickingmybutt!

    Here's the second one . . .



    Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram,
    the parallelogram is a rhombus.

    Given: ABCD is a parallelogram with \angle1 = \angle2

    To Prove: ABCD is a rhombus.

    We need to prove that two adjacent sides are equal.


    Code:
              A * - - - - - - - - * B
               /2 * 1            /
              /     *           /
             /        *        /
            /           *     /
           /            3 * 4/
        D * - - - - - - - - * C

    1.\;\angle1 = \angle 2. . . . . . . . . . \text{Given}

    2.\;AB \parallel DC,\:AD \parallel BC. . \text{d{e}f. parallelogram}

    3.\;\angle1 = \angle 3,\:\angle 2 = \angle 4. . . \text{alt-int. angles}

    4.\;\angle1 \,=\,\angle 4. . . . . . . . . \text{Transitivity}

    5.\;\Delta ABC\text{ is isosceles}. . . \text{d{e}f. isosceles}

    6.\;\therefore\:AB = BC. . . . . . \text{d{e}f. isosceles}

    . . . Q.E.D.

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  3. #3
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    Oh Thank you SOOOOO much!!!

    =D!!
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  4. #4
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    Hello, proofsRkickingmybutt!

    Prove that the tangents to a circle at the endpoints of a diameter are parallel.
    State what is given, what is to be proved, and your plan of proof.
    Then write a two-column proof.
    Code:
                    A
        P - - - - * * * - - - - Q
              *     |     *
            *       |       *
           *        |        *
                    |
          *         |         *
          *         *O        *
          *         |         *
                    |
           *        |        *
            *       |       *
              *     |     *
        R - - - - * * * - - - - S
                    B

    There is a Theorem that says:
    . . If a line is tangent to a circle, the radius drawn to
    . . the point of tangency is perpendicular to the tangent.

    We have a circle with center O and diameter AB.

    Line PQ is tangent to circle O at A.
    Line RS is tangent to circle O at B.


    1.\;OA \perp PQ,\:OB \perp RS . . . . . \text{Theorem}

    2.\;\angle OAP = 90^o,\:\angle OBS = 90^o . . \text{d{e}f. perpendicular}

    3.\;\angle OAP = \angle OBS. . . . . . . . . \text{All right angles are equal.}

    4.\;\therefore\:PQ \parallel RS. . . . . . . . . . . \text{alt-int. angles}

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  5. #5
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    Quote Originally Posted by proofsRkickingmybutt View Post

    Given: In triangle ABC, (angle) B = 120 degrees

    Prove: Angle A is not equal to 60 degrees

    Plan: Use an indirect proof.

    NOTE: Write the proof using the paragraph method.
    I'm guessing it's too trivial to say that if B is 120 degrees, and A is 60 degrees, then C must be equal to 180 (total number of degrees in a triangle) - 180 = 0... which is clearly nonsense... and therefore A is less than or at least, not equal to 60?

    Edit: Unless you're supposed to prove the sum of the angles in a triangle = 180 degrees... but that's been done to death
    Last edited by Unenlightened; February 3rd 2009 at 07:39 PM. Reason: ..
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