Proposition: 6.04: Equiangular Triangles are Similar
(Proposition 4 from Book 6 of Euclid's “Elements”)
In equiangular triangles the sides about the equal angles are proportional, and those (sides) subtending equal angles correspond.
- Let ABC and DCE be equiangular triangles, having angle ABC equal to DCE, and (angle) BAC to CDE, and, further, (angle) ACB to CED.
- I say that in triangles ABC and DCE the sides about the equal angles are proportional, and those (sides) subtending equal angles correspond.

Modern Formulation
Equiangular triangles are similar.
Table of Contents
Proofs: 1
Mentioned in:
Definitions: 1
Proofs: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Propositions: 18
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References
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016