Corollary: Equivalent Statements Regarding Parallel Lines
(related to Proposition: 1.29: Parallel Lines III)
Suppose two straight lines are intersected by a third straight line at one and only one point. The two straight lines are parallel if and only if any one of these three properties hold:
 corresponding alternate angles are equal;
 exterior angles equal their corresponding interior angles;
 exterior angles equal their corresponding interior angles;
Table of Contents
Proofs: 1
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclidâ€™s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"