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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:

1. corresponding alternate angles are equal;
2. exterior angles equal their corresponding interior angles;
3. exterior angles equal their corresponding interior angles;

Table of Contents

Proofs: 1

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References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"