Special Triangles: Classifying Triangles

Parts of Triangles

Every triangle has three sides and three angles. In the following lessons we'll refer to certain sides as opposite sides, and certain angles as included angles. It's important to understand these definitions as early as possible. A side is opposite an angle, or a vertex, if neither of the endpoints of that side are at the vertex of the specified angle. An angle is included between two sides if the common endpoint of the sides is the vertex of the angle. Below these concepts are pictured.

Figure %: A generic triangle, triangle ABC

In triangle ABC above, side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C. Angle A is included in sides b and c, angle B is included in sides a and c, and angle C is included in sides a and b.

When triangles are classified according to the lengths of their sides, they fit into one of three categories: scalene, isosceles, or equilateral. If none of the sides of a triangle are equal (of equal length), the triangle is scalene. If two or more of the triangles sides are equal, the triangle is isosceles. If all three of the sides of a triangle are equal, it is equilateral. All equilateral triangles are also isosceles, by definition.

Figure %: A scalene, isisceles, and equilateral triangle

When triangles are classified by their angles, they fit into one of four categories: acute, obtuse, right, or equilateral. If the angles of a triangle are all acute, the triangle is acute. If a triangle has one obtuse angle (remember that one is the maximum number of obtuse angles a triangle can have), it is an obtuse triangle. If a triangle has one right angle, it is a right triangle. And if all three angles of a triangle are congruent, or equal, then it is an equiangular triangle.