Right triangle altitude to the hypotenuse is related to the legs of the right triangle by For solutions of this equation in integer values of "a, b, f", and "c", see here. The altitude from either leg coincides with the other leg. Since these intersect at the right-angled vertex, the right triangle's orthocenter—the intersection of its three altitudes—coincides with the right-angled vertex. The Pythagorean theorem states that: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are 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