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Math Help - Prove that two lines are parallel in a given geometry

  1. #1
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    Prove that two lines are parallel in a given geometry

    Attached are the question and solution for part (a) and (b).

    For part (c), how to prove that EF is parallel to AC?

    Thank you.
    Attached Thumbnails Attached Thumbnails Prove that two lines are parallel in a given geometry-question.jpg   Prove that two lines are parallel in a given geometry-partial-solution-b-.jpg  
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  2. #2
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    Re: Prove that two lines are parallel in a given geometry

    Hi Yeoky,
    Complete the following constructions to your drawing

    Extend BH to AD @ J BG to DC @K
    connect JK,JE,KF,JE, EK

    There are congruencies leading to BG= HD BH= GD BHDG is a parallelogram
    Also EJ =FK EF=JK EJKF is a parallelogram
    The perpendicular distance from AC to EF and JK are equal
    EF is parallel to AC.

    Find the congruent parts
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  3. #3
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    Re: Prove that two lines are parallel in a given geometry

    Its very simple just prove that figure a parallelogram by joining its all sides and diagonals.This will prove that the difference of two lines is equal at every point.
    sin cos tan table
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