Definition:Triangle (Geometry)/Equilateral

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An equilateral triangle is a triangle in which all three sides are the same length:

That is, a regular polygon with $3$ sides.


Thus it can be seen that an equilateral triangle can be considered to be a special case of an isosceles triangle.

Euclid's Definition

In the words of Euclid:

Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.

(The Elements: Book $\text{I}$: Definition $20$)

Also known as

An equilateral triangle is also less commonly known as an equiangular triangle.

Also see

  • Results about equilateral triangles can be found here.