Triangle inequality ≥ b ≥ c" and "formula_8" is the golden ratio, as In the case of right triangles, the triangle inequality specializes to the statement that the hypotenuse is greater than either of the two sides, and less than their sum. The second part of this theorem is already established above for any side of any triangle. The first part is established using the lower figure. In the figure, consider the right triangle . An isosceles triangle is constructed with equal sides . From the triangle postulate, the angles in the right triangle satisfy: Likewise, in the isosceles triangle , the
Special right triangle within a regular icosahedron of side length "c": the shortest line segment from any vertex "V" to the plane of its five neighbors has length "a", and the endpoints of this line segment together with any of the neighbors of "V" form the vertices of a right triangle with sides "a", "b", and "c". Special right triangle A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called