III.

Spherical Triangles

Many properties of plane triangles have analogues in spherical triangles, but the differences between the two types are important. For example, the sum of the angles of a spherical triangle is between 180° and 540° and varies with the size and shape of the triangle. A spherical triangle with one, two, or three right angles is called a rectangular, birectangular, or trirectangular triangle. A spherical triangle in which one, two, or three sides are quadrants (quarter circumferences) is called a quadrantal, biquadrantal, or triquadrantal triangle. See also Sphere.