|Book I Proposition 27|
For, if not, AB, CD when produced will meet either in the direction of B, D or towards
Let them be produced and meet, in the direction of B, D, at G.
Then, in the triangle GEF,
the exterior angle AEF is equal to the interior and opposite angle EFG: which is impossible. [Prop.16]
AB, CD when produced will not meet in the direction B, D.
Similarly it can be proved that neither will they meet towards A, C.
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