# 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.

Proofs: 1

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)

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

#### Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016