特殊直角三角形是一些有特殊性质的直角三角形，其特殊性质可能是使三角形的计算更加方便，或是存在一些较简单的公式。例如有些三角形的内角有一些简单的关系，例如45–45–90度三角形，这是各角有特殊关系的直角三角形。也有些直角三角形的各边有特殊关系，例如各边的比例可以用自然数表示，例如3 : 4 : 5，或是可以用黄金比例表示等。若在处理这些三角形时知道其特殊的边关系或角关系，可以快速的计算一些几何问题而不需用到一些较复杂的公式。

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 an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods.