Lesson 62: Classifying Triangles

New Concept

Triangles can be classified by their angles (acute, right, obtuse) or by their sides (equilateral, isosceles, scalene).

Equilateral triangle

• Three equal sides
• Three equal angles

Isosceles triangles

• At least two sides have the same length.
• At least two angles have the same measure.

Property

An equilateral triangle has three equal sides and three equal angles. Each angle measures $60^\circ$.

Examples

A triangle with side lengths of 8 cm, 8 cm, and 8 cm is equilateral.
If the perimeter of an equilateral triangle is 36 inches, each side must be $36 \div 3 = 12$ inches long.
Any triangle with three $60^\circ$ angles is guaranteed to be an equilateral triangle.

Explanation

Think of this as the perfectly balanced triangle! Because all the sides are the same length, the angles have to split the total $180^\circ$ equally. So each angle is always $60^\circ$.

Property

An isosceles triangle has at least two sides of the same length and at least two angles of the same measure.

Examples

A triangle with angles measuring $70^\circ$, $70^\circ$, and $40^\circ$ is an isosceles triangle.
In $\triangle ABC$, if side $\overline{AB}$ is the same length as side $\overline{AC}$, then $\angle C$ is equal to $\angle B$.
An isosceles right triangle has one $90^\circ$ angle and two $45^\circ$ angles.

Explanation

Isosceles triangles are all about pairs! If a triangle has two identical sides, then the angles sitting opposite those sides are also twins. It’s a geometric two-for-one special on sides and angles.

Property

A scalene triangle has all sides of different lengths and all angles of different measures.

Examples

A triangle with side lengths of 5 cm, 7 cm, and 8 cm is a scalene triangle.
A triangle with angles measuring $30^\circ$, $60^\circ$, and $90^\circ$ is a scalene triangle.

Explanation

Meet the scalene triangle, the king of being unique! Every side has a different length, which means every angle has a different measure. No repeats, no matches, just three different sides and angles.