...le BCE is a Euclidean triangle, it has an angle sum of 180º, and ∠BCE + ∠BEC = ∠EBA (an exterior angle). The angle sum of the 2-gon AB is ∠EAB + ∠EB... ... ∠EBY and ∠BEX must be congruent. Since the alternate interior angles ∠BEX and ∠EBA must be congruent, we have that ∠EBA and ∠EBY are congruent. It ... ...nter-example, but there might be other ways that this axiom fails. That angles ∠EBA and ∠EBY are congruent assumed that both pairs of alternate inter... ...s, and the SAS theorem must hold for these triangles. It follows that ∠EBY and ∠EBA are congruent, and that Y must lie on a. We now have that X and ...