Equilateral triangle

In geometry, an equilateral triangle is a triangle where all three sides are the same length and all three angles are also the same and are each 60°.
If an altitude is drawn, it bisects the side to which it is drawn, in turn leaving two separate 30-60-90 triangles
Principal properties.
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 have simple relationships to the altitude ("h") of each vertex from the opposite side:
In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors and the medians to each side coincide.
Equal cevians.
Three kinds of cevians are equal for (and only for) equilateral triangles:
Coincident triangle centers.
Every triangle center of an equilateral triangle coincides with its centroid, which implies that the equilateral triangle is the only triangle with no Euler line connecting some of the centers. For some pairs of triangle centers, the fact that they coincide is enough to ensure that the triangle is equilateral. In particular:
Six triangles formed by partitioning by the medians.
For any triangle, the three medians partition the triangle into six smaller triangles.