Proposition: 1.06: Isosceles Triagles II

(Proposition 6 from Book 1 of Euclid's “Elements”)

If a triangle has two angles equal to one another then the sides subtending the equal angles will also be equal to one another.


Modern Formulation

If a given triangle has two equal angles, then the sides opposite the two angles are equal in length (i.e., the triangle is isosceles).

Proofs: 1 Corollaries: 1

Proofs: 1 2 3 4 5 6 7 8 9 10 11

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"