Golden triangle (mathematics) Golden triangle (mathematics) A golden triangle, also known as the sublime triangle,is an isosceles triangle in which the duplicated side is in the golden ratio to the distinct side: Golden triangles are found in the nets of several stellations of dodecahedrons and icosahedrons. Also, it is the shape of the triangles found in the points of pentagrams. The vertex angle is equal to Since the angles of a triangle sum to 180°, base angles are therefore 72° each. The golden triangle can also be found in a regular decagon, or an equiangular and equilateral ten-sided polygon, by connecting any two
Isosceles triangle not true for other triangles. If any two of an angle bisector, median, or altitude coincide in a given triangle, that triangle must be isosceles. The area formula_5 of an isosceles triangle can be derived from the formula for its height, and from the general formula for the area of a triangle as half the product of base and height: The same area formula can also be derived from Heron's formula for the area of a triangle from its three sides. However, applying Heron's formula directly can be numerically unstable for isosceles triangles with very sharp angles, because of the