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 its sides be in a geometric progression. The 3–4–5 triangle is the unique right triangle (up to scaling) whose sides are in an arithmetic progression. Let be the side length of a regular decagon inscribed in the unit circle, where "φ" is the golden ratio. Let be the side length of a regular hexagon in the unit circle, and let {2}}</math>}} be the side length of a regular pentagon in the unit circle. Then , so these three lengths form the sides of a right triangle. The same triangle forms half of a golden rectangle. It may also be found