Proposition: 1.20: The Sum of the Lengths of Any Pair of Sides of a Triangle (Triangle Inequality)

(Proposition 20 from Book 1 of Euclid's “Elements”)

In any triangle, (the sum of) two sides taken together in any (possible way) is greater than the remaining (side).


Modern Formulation

see triangle inequality.

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8
Propositions: 9
Sections: 10

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"