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Math Help - Geometry, Triangle Proof!

  1. #1
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    Geometry, Triangle Proof!

    Hey Guys!

    I have a proof here with me and I just want to see if I am correct.

    So we're trying to prove these triangles are congruent and then apply the CPCTC method to prove Segment FG is congruent to segment HJ.

    This is what I have so far: (I mentioned HG is congruent to HG and KJ is congruent to KJ by Identity, but I'm not sure if I can conclude these triangles are congruent after that)

    Proof and Reasons:

    1) Angle 1 is congruent to Angle 2 ------- 1) Given
    2) Line segment FH is congruent to Line segment HK --------- 2) The Midpoint of a line segment forms 2 congruent segments
    3) Line segment HG is congruent to HG, line segment KJ is congruent to KJ ----------- 3) Identity
    4) Triangle FHG is Congruent to Triangle HKJ ----------- 4) SAS
    5) Line segment FG is congruent to Line segment HJ ------- 5) CPCTC
    Attached Thumbnails Attached Thumbnails Geometry, Triangle Proof!-screen-shot-2013-10-22-11.47.59-pm.png  
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  2. #2
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    Re: Geometry, Triangle Proof!

    ∠ FHG= ∠ HKJ ------Given
    FH = HK Because H is midpoint of FK
    FG ∥HJ Given thus
    ∠ HFG = ∠ KHJ Corresponding angles
    Hence the triangle FHG is congruent to HKJ by ASA criterion
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  3. #3
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    Re: Geometry, Triangle Proof!

    Hey ibdutt,

    When 2 lines are parallel, are their sides also congruent? Or are the lines just parallel?
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  4. #4
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    Re: Geometry, Triangle Proof!

    A line cannot be measured and if we cannot measure we can't say that they are congruent. So the lines are parallel.
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