Corollary: Existence of Parallel Straight Lines

(related to Proposition: 1.16: The Exterior Angle Is Greater Than Either of the Non-Adjacent Interior Angles)

If the segments \(\overline{BA}\) and \(\overline{CF}\) used to prove the proposition 1.16 were extended to straight lines \(BA\) and \(CF\), those straight lines could not meet at any finite distance. In other words, they are parallel. Fig5p5p19_1

Proofs: 1

Axioms: 1
Definitions: 2

Thank you to the contributors under CC BY-SA 4.0!



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"