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Thread: Two-Column proof with triangles, theorems?

  1. #1
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    Two-Column proof with triangles, theorems?

    Man I hate proofs.

    Two-Column proof with triangles, theorems?-proof.gif
    Given: segment AS//BT, and <4 congruent to <5
    Prove: <1 congruent to <2

    I would really appreciate if anyone could show the steps and theorems you used to solve this (we all know how proofs work)
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  2. #2
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    Re: Two-Column proof with triangles, theorems?

    There's only one tricky bit.

    Because AS || BT we know <5 =<2

    let <4 = <5 = x

    working in degrees

    2x+<3 = 180 as the sum of interior angles of a triangle is 180 degrees

    <1 + <2 + <3 = 180 as these angles make up a straight angle

    subtract the 1st from the 2nd equation

    <1 + <2 - 2x = 0

    <1 + <2 = 2x

    Now <5=<2 = x

    <1 + x = 2x

    <1 = x

    <1 = x = <2

    <1 = <2
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  3. #3
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    Re: Two-Column proof with triangles, theorems?

    Hello, funnyguy287!

    I don't have a two-column proof.
    I'll show you my steps.
    I'll let you break it up into Statements and Reasons.


    \text{Given: }\:AS \parallel BT,\;\;\angle 4 = \angle 5
    \text{Prove: }\:\angle 1 = \angle 2.

    Code:
                                  B
                                  *
                               *6*5*
                            *   *   *
                     A   *     *     *
                      *       *       *
                   *   *     *         *
                *       * 2 *           *
             *         1 * * 3         4 *
          * * * * * * * * * * * * * * * * *
          R               S               T

    Since AS \parallel BT,\;\angle1 = \angle4.

    In \Delta SBT,\:\angle 3 + \angle 4 + \angle 5 \:=\:180^o \quad\Rightarrow\quad \angle 3 \:=\:180^o - 2\angle 4


    We have: . \angle RST \:=\:180^o

    . . \angle1 + \angle2 +\angle3 \:=\:180^o

    . . \angle 4 + \angle 2 + (180^o-2\angle4) \:=\:180^o

    . . \angle2 - \angle4 \:=\:0 \quad\Rightarrow\quad \angle 2 = \angle 4


    Since \angle1 = \angle4, we have: . \angle1\,=\,\angle2

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  4. #4
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    Re: Two-Column proof with triangles, theorems?

    given BS=BT AS parallel to BT a for angle
    1 a2=a4
    2a1=a5
    3a4=a5
    a1=a4
    a1=a2
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