Equilateral triangle

An equilateral triangle is a triangle, the three sides are all the same length. Then - the triangle - all three angles equal and amount to 60 °. Equilateral triangles are also equiangular or so regular triangles, they are also called regular triangles. All equilateral triangles are similar to each other. Equilateral triangles are rotationally symmetric ( with respect to rotations around the center by 120 ° or multiples thereof ), mirror symmetry (with respect to the perpendicular bisector ) and acute angle. Your isometry group is the dihedral group. The plane is pflasterbar with equilateral triangles.

Calculation and design

An equilateral triangle is completely determined by a side length (see congruence ).

Excellent points

In an equilateral triangle, fall height, perpendicular bisector ( Seitensymmetrale ) Seitenhalbierende ( gravity line) and bisector to one side in each case together. Hence the orthocenter, the circumcenter, the center of gravity and the incenter are the same point. This center shares the routes in a 2:1 ratio.