Parallelogram Question Writing a Proof

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given: segment SV is parallel to segment TU and
triangle SVX is congruent to triangle UTX

[the figure has a V on the top left corner, U on the top
right corner, X in the middle of four triangles inside
and S on the bottom left and T on the bottom right]

prove VUTS is a parallelogram

Thank You, I appreciate it! :) =) ^_^

  • Parallelogram Question Writing a Proof -

    SV parallel to UT

    for convenience call angle SVX=UTX = A
    but then VXT is a straight line (opposite interior equal angles A cutting parallel lines SV and UT)
    similarly line SXU is a straight line.
    then we know angle SXV = TXU = C
    then C + angle VXU = C + angle SXT = 180
    so
    angle VXU = angle SXT and those triangles are congruent (SAS)
    That means for example angle UVX =STX
    and therefore angle SVU = STU
    therefore parallelogram (opposite angles equal)

  • Parallelogram Question Writing a Proof -

    Thank you for not only answering my question but helping me understand! Thank you I greatly appreciate your help! :)

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