As the lesson title indicates, there are many types of triangles that are classified by their sides, angles, or both. Each type is distinguished by some properties from the other types.

It is worth noting that triangles are among the important shapes in geometry and algebra together and have many uses for solving mathematical and physical problems.

In this lesson, we will try to explain each type of triangle with the shapes, definitions and properties, and at the end you will be able to understand the difference between them.

Triangles are classified according to the measure of sides and measures of angles. The two properties common to all triangles are that the sum of the angles of a triangle is 180 degrees, and the sum of the lengths of the two sides of a triangle is greater than the length of the third side. The following are the distinguishing characteristics of each type of triangle according to classification.

**By Side:**

Equilateral Triangle

Isosceles Triangle

Scalene Triangle

**By Angle:**

Acute-Angled Triangle

Right-Angled Triangle

Obtuse-Angled Triangle

For this type of triangle, we'll only be concerned with the sides of the triangle. As you well know, any triangle is determined from three sides, and these sides can be all isometric, or only two isometric sides, or the three sides of different lengths.

**Equilateral Triangle:** the three sides are equal (isometric).

**Isoscele Triangle:** only two of the sides, called the **legs**, must have the same measure. The other side is called the **base**.

**Scalene Triangle:** is uneven, no side is the same length as any other. To be more precise,“scalene” means “not
equilateral or isosceles.

In this classification, we will only study the angles of a triangle. As you know, any triangle has three angles. All of these angles can be acute, one obtuse and the two other acute, or one right angle and the two other acute.

**Acute Triangle:** all angles are acute (less than 90°).

**Obtuse Triangle:** has an angle obtuse (more than 90°), and two acute angles.

**Right Triangle:** has a right angle (90°), and two acute angles.

Triangles can also be categorized by both angles and sides. In this case, we will have seven different states all derived from the above classifications.

**Equilateral or Regular Triangle:** In this triangle, all the sides are congruent and all the angles are congruent. Each angle measures 60°.

**Isosceles Right Triangle:** This triangle has two congruent sides and a right angle. The two acute angles at the *base* are congruent, and their measure is 45°.

**Obtuse Isosceles Triangle:** This triangle has two congruent sides and an obtuse angle. The two acute angles at the *base* are congruent, measuring less than 45°.

**Acute Isosceles Triangle:** This triangle has two congruent sides and an acute angle. The two acute angles at the *base* are congruent, measuring greater than 45°.

**Right Scalene Triangle:** This triangle has a right angle and all sides are not congruent.

**Obtuse Scalene Triangle:** This triangle has an obtuse angle and all sides are not congruent.

**Acute Scalene Triangle:** This triangle has an acute angle and all sides are not congruent.