## equilateral triangle

### a triangle with 3 congruent sides

An equilateral triangle is a triangle in which all three sides are of equal length and all three angles are also of equal measure, which is 60 degrees each. Some important properties of an equilateral triangle are:

1. Equal sides: All three sides of an equilateral triangle are congruent, which means they are of equal length.

2. Equal angles: All three angles of an equilateral triangle are congruent, which means they are of equal measure.

3. Perimeter: The perimeter of an equilateral triangle is the sum of the lengths of its three sides. If a side of the triangle is denoted by a, then the perimeter (P) is given by P = 3a.

4. Area: The area of an equilateral triangle can be found using the formula A = (sqrt(3)/4) x a^2, where A is the area and a is the length of a side.

5. Height: The height of an equilateral triangle is the perpendicular distance from any vertex to the opposite side. It can be found using the formula h = (sqrt(3)/2) x a, where h is the height and a is the length of a side.

6. Circumcenter: The circumcenter of an equilateral triangle is the point where the perpendicular bisectors of the sides meet. It is equidistant from all three vertices of the triangle.

7. Incenter: The incenter of an equilateral triangle is the point where the angle bisectors of the angles meet. It is equidistant from all three sides of the triangle.

Equilateral triangles have many interesting properties and are commonly used in both mathematics and real-world applications.

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