### Topic Page: Triangle

**triangle**from

*The Penguin Dictionary of Science*

**triangle, in mathematics**from

*The Columbia Encyclopedia*

in mathematics, plane figure bounded by three straight lines, the sides, which intersect at three points called the vertices. Any one of the sides may be considered the base of the triangle. The perpendicular distance from a base to the opposite vertex is called an altitude. The area of a triangle is equal to one half the product of the base and the corresponding altitude. The line segment joining the midpoint of a side to the opposite vertex is called a median. All three altitudes of a triangle go through a single point, and all three medians go through a single (usually different) point. In Euclidean geometry the sum of the angles of a triangle is equal to two right angles (180°). If all three angles of a triangle are equal, the triangle is called equilateral. An isosceles triangle has two equal angles. A scalene triangle is one in which all three angles are different. A right triangle has one right angle. In geometry it is shown that two triangles are congruent (i.e., are the same shape and size) if, in general, any three independent parts (sides or angles) of one are the same as the corresponding three parts of the other. The rules of congruency make it possible, in trigonometry, to compute the sides and the angles of a triangle when three of these values are known. The triangle is the simplest of the polygons (i.e., it has the least possible number of sides). Since any polygon can be broken up into triangles by drawing various diagonals, a complete theory of the measurement of triangles provides a complete theory of the measurement of all polygons. In non-Euclidean geometries, the angles of a triangle are either less than two right angles (hyperbolic geometry) or more than two right angles (elliptic geometry).

### Images

### Video

### Related Credo Articles

##### Full text Article triangle

A plane closed figure formed by three line segments (the sides) joining three points (the vertices). Triangles are classified according to the...

##### Full text Article triangle

pronunciation (14c) 1 : a polygon having three sides compare spherical triangle 2 a : a percussion instrument consisting of a rod of steel bent int

##### Full text Article triangle

/trieanggl/ noun 1 a polygon with three angles and three sides. 2 something shaped like a triangle. 3 a percussion...