A triangle is a closed figure formed by connecting three non-collinear points, called vertices, by line segments to result in three sides and three interior angles (hence the word "tri-angle"). If the three angles all lie in the same plane, the triangle is called a plane, or Euclidean, triangle. If the three angles do not all lie in the same plane, the triangle is called a spherical, or curvilinear, triangle. The word triangle, by itself, is usually taken to mean a plane triangle, while a curvilinear triangle is stated as such. The triangle is the simplest polygon because it is the closed figure having the fewest number of angles and sides. The word triangle can be traced back to the Latin "triangulum", and to the neuter of "triangulus" (three-angled).

Some important facts and definitions pertaining to triangles are:

• Any one of the sides of a triangle may be...