Definition: 1.20: Equilateral Triangle, Isosceles Triangle, Scalene Triangle
And of the trilateral figures: an equilateral triangle is that having three equal sides, an isosceles (triangle) that having only two equal sides, and a scalene (triangle) that having three unequal sides.
Modern definitions
A triangle is called:
- equilateral, if it has three congruent sides (equivalently, of which all sides are equal in length),
- isosceles, if it has two congruent sides (equivalently, with only two equal sides),
- scalene, if it has no congruent sides, (equivalently whose three sides are unequal in length).
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.
- The term "equal" has two different meanings in Euclid's “Elements”: congruence and equality. In this case, "congruent sides" are meant. Alternatively, we could use "equal lengths of sides" rather than "equal sides".
Examples
An equilateral triangle:
An isosceles triangle:
A scalene triangle:
Table of Contents
- Definition: Altitude of a Triangle
Mentioned in:
Corollaries: 1
Definitions: 2 3 4
Motivations: 5
Problems: 6 7
Proofs: 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Propositions: 25 26 27 28
Solutions: 29 30 31
Thank you to the contributors under CC BY-SA 4.0! 
- Github:
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- non-Github:
- @Calahan
- @Casey
- @Fitzpatrick
References
Adapted from CC BY-SA 3.0 Sources:
- Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
- Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
