A triangle is a closed three-sided, three-angled figure, and is the simplest example of what mathematicians call polygons (figures having many sides). Triangles are among the most important objects studied in mathematics owing to the rich mathematical theory built up around them in Euclidean geometry and trigonometry, and also to their applicability in such areas as astronomy, architecture, engineering, physics, navigation, and surveying.

In Euclidean geometry, much attention is given to the properties of triangles. Many theorems are stated and proved about the conditions necessary for two triangles to be similar and/or congruent. Similar triangles have the same shape but not necessarily the same size, whereas congruent triangles have both the same shape and size.

One of the most famous and useful theorems in mathematics, the Pythagorean Theorem, is about triangles. Specifically, the Pythagorean Theorem is about right triangles, which are triangles having a 90° or "right" angle...