Posted by **aLEXANDRIA** on Sunday, January 8, 2012 at 3:14pm.

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 -
**Damon**, Sunday, January 8, 2012 at 4:25pm
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 -
**aLEXANDRIA**, Sunday, January 8, 2012 at 6:52pm
Thank you for not only answering my question but helping me understand! Thank you I greatly appreciate your help! :)

- Parallelogram Question Writing a Proof -
**dickulees**, Sunday, January 31, 2016 at 12:12pm
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