◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--1-plane-geometry / Definition: 1.21: Right Triangle, Obtuse Triangle, Acute Triangle

Definition: 1.21: Right Triangle, Obtuse Triangle, Acute Triangle

And further of the trilateral figures: a right-angled triangle is that having a right angle, an obtuse-angled (triangle) that having an obtuse angle, and an acute-angled (triangle) that having three acute angles.

Modern definition

A triangle with: * a right angle is called right-angled (or right), * one obtuse angle is called obtuse-angled (or obtuse), * three acute angles is called acute-angled (or acute).

Notes

• Euclid implicitly renames the term "3-sided figure" to the term "triangle", and defines special kinds of triangles, without defining the general term "triangle". However, this term is used frequently in Euclid's “Elements” in its general meaning.

Examples

A right triangle:

An acute triangle:

A obtuse triangle:

Mentioned in:

Corollaries: 1 2
Definitions: 3 4
Lemmas: 5
Proofs: 6 7 8 9 10 11 12 13 14
Propositions: 15 16 17 18
Solutions: 19 20
Topics: 21

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References

Adapted from (subject to copyright, with kind permission)

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