Proposition: 1.15: Opposite Angles on Intersecting Straight Lines

(Proposition 15 from Book 1 of Euclid's “Elements”)

If two straight lines cut one another then they make the vertically opposite angles equal to one another.


Modern Formulation

If two straight lines \(AB\) and \(CD\) intersect one another at one point \(E\), their opposite angles are equal.

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8

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"

Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"