# Parallelogram Question Writing a Proof

posted by on .

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! :)