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.
![fig13e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book01/fig13e.png?raw=true)
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
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References
Adapted from CC BY-SA 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"