Triangles have three sides, which is their most recognizable characteristic and the quality that distinguishes them from any other shape. Each side is a line. When three or more lines come together, meeting at common points, they form a closed figure. The lines may be of any length as long as they all intersect. Therefore, triangles do not occur in just one form, like circles.
The inside of every triangle has three wedge-shaped corners called angles. Angles are measurable in units called degrees. The combined measurement of all three angles always equals 180 degrees. It is mathematically impossible for three lines forming a closed figure to have angles adding up to any other sum (in degrees).
When a person categorizes a triangle based on the size of (the number of degrees forming) its angles, it can fall into one of four categories. When all three angles are of the same size, they form an equilateral triangle. When all three angles are less than 90 degrees, they form an acute triangle. If one of the angles is more than 90 degrees, the lines form an obtuse triangle. Finally, if one angle is 90 degrees, it is a right angle, and all three angles together form a right triangle.
When a person categorizes a triangle based on the length of its sides, it can fall into one of three categories. Since equilateral triangles have the same angle measurements, each line has the same length, too. When a triangle has two sides of the same length, it is an isosceles triangle. If all three sides are of different lengths, they form a scalene triangle.