Triangles can be classified either according to their sides or according to their angles. All of each may be of different or the same sizes; any two sides or angles may be of the same size; there may be one distinctive angle.
The types of triangles classified by their sides are the following:
- Equilateral triangle: A triangle with all three sides equal in measure. In Figure 1, the slash marks indicate equal measure.
Figure 1 Equilateral triangle
- Isosceles triangle: A triangle in which at least two sides have equal measure (Figure 2).
Figure 2 Isosceles triangles
- Scalene triangle: A triangle with all three sides of different measures (Figure 3).
Figure 3 Scalene triangle
The types of triangles classified by their angles include the following:
- Right triangle: A triangle that has a right angle in its interior (Figure 4).
Figure 4 Right triangle
- Obtuse triangle: A triangle having an obtuse angle (greater than 90° but less than 180°) in its interior. Figure 5 shows an obtuse triangle.
Figure 5 Obtuse triangle
- Acute triangle: A triangle having all acute angles (less than 90°) in its interior (Figure 6).
Figure 6 Acute triangle.
- Equiangular triangle: A triangle having all angles of equal measure (Figure 7).
Figure 7 Equiangular triangle
Because the sum of all the angles of a triangle is 180°, the following theorem is easily shown.
Theorem 27: Each angle of an equiangular triangle has a measure of 60°.