Equilateral triangle

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An equilateral triangle has, by definition, three sides that are equal in length.

In classical geometry it can easily be proved that an equilateral triangle is also equiangular, that is each of its three angles is equal; since another theorem states that the three angles of a triangle total 180°, each angle is 60°.

In some geometries (like sphere surface geometry) an equilateral triangle can have angles being more than 60° each: for example the North pole, the point situated 0°N 0°E and the point situated 0°N 90°E form an equilateral triangle with angles of 90°. This can be seen pointing for example the North Pole, Sao Tome & Principe and Singapore on a globe.

Note that it is only triangles that have the characteristic that equilateral means equiangular. For polygons of more than three sides, this is not true. A quadrilateral can have four equal sides—be a rhombus—without necessarily being a square.

See also