# 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:

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!

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### References

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

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014