Classify triangles by side lengths

Triangles are classified by the equality relationships among their side lengths: scalene triangles have no equal sides, isosceles triangles have exactly two equal sides, and equilateral triangles have three equal sides. The classification depends on measured or stated side lengths rather than a triangle’s apparent orientation, size, or angle measures, and provides a foundation for reasoning about symmetry, congruence, and related angle relationships.

Detailed Explanation: Classify triangles by side lengths

To classify a triangle by its side lengths, compare the lengths of all three sides.

Scalene: all three sides have different lengths.
Isosceles: exactly two sides have the same length.
Equilateral: all three sides have the same length.

Example

A triangle has side lengths $7\text{ cm}$ , $5\text{ cm}$ , and $7\text{ cm}$ . Classify the triangle.

List the side lengths:

7\text{ cm},\ 5\text{ cm},\ 7\text{ cm}

Compare the lengths. Two sides are equal:

7\text{ cm}=7\text{ cm}

The third side is different, so all three sides are not equal.
Therefore, the triangle is isosceles.

The triangle’s position, size in a drawing, or angle measures do not affect its classification. Use only the side lengths.

Learn by doing: Classify triangles by side lengths

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Triangle Classification - Sides

Earned ?