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°.