Proposition: 1.13: Angles at Intersections of Straight Lines
(Proposition 13 from Book 1 of Euclid's “Elements”)
If a straight line stood on a(nother) straight line makes angles, it will certainly either make two right angles, or angles whose sum is) equal to two right angles.
Modern Formulation
If the straight line \(AB\) intersects the straight line \(CD\) at one and only one point (\(B\)), then either \(\angle{ABC}\) and \(\angle{DBA}\) are right angles or the sum \(\angle{ABC}+\angle{DBA}\) equals the sum of two right angles.
Table of Contents
Proofs: 1 Corollaries: 1 2
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9 10 11
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Calahan
 @Casey
 @Fitzpatrick
References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"