Proof of Parallelogram Theorem: 2 Pairs of Opposite Angles Congruent

[macaholic]

Proof of parallelogram theorem "If 2 pairs of opposite angles congruent, then par..."

I was just wondering, why exactly does "If 2 pairs of opposite angles congruent" prove that a quadrilateral is a parallelogram? Does it have something to do with the fact that the sum of the interiors equals 360, so 2x+2y=360? I like knowing why the theorems work, so if anyone knows the proof for this I would love to see it.

 

[Office_Shredder]

if 2x+2y=360, then x+y=180. This pretty much does it, as if you draw three sides of the parallelogram, for the two angles formed to sum to 180, they must be interior angles. Hence, the opposite edges you've drawn are parallel.

 

[Chris Hillman]

This is a fine example for automatic theorem proving using Groebner basis methods, but I guess that is OT...