Equilateral triangle Equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Denoting the common length of the sides of the equilateral triangle as "a", we can determine using the Pythagorean theorem that: Denoting the radius of the circumscribed circle as "R", we can determine using trigonometry that: Many of these quantities
Automedian triangle sharing no common factor) as with formula_4 and formula_5 coprime, formula_6 odd, and to satisfy the triangle inequality formula_7 (if the quantity inside the absolute value signs is negative) or formula_8 (if that quantity is positive). Then this triangle’s medians formula_9 are found by using the above expressions for its sides in the general formula for medians: where the second equation in each case reflects the automedian feature formula_11 From this can be seen the similarity relationships There is a primitive integer-sided automedian triangle that is not generated from a right triangle: namely, the equilateral triangle with sides of unit