Fellow Mathers, to any who could provide an insightful proof as to why this is true, Thank You.
Lines are Parallel iff their Corresponding Angles amongst a Traversal are Congruent.
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Definitions/Axioms used:
• Traversal: a line T such that given two other lines J and I: (T⋂J)⋃(T⋂I)= {Pj , Pi}
• Corresponding Angles: Given this traversal create 8 angles, the corresponding angles here are the ones that: (a) do not share a vertex, (b) lie on the same side of T, & (c) if one angle is in the interior of the two lines, the other is its exterior.
• Parallel Line: a line G is parallel to another line F if: F⋂G=ϕ
• Thru any point P not collinear to another line L, there exists one and only one line thru P parallel to L. (Parallel Postulate)