Complete Guide to the Different Types of Triangles

Types of Triangles: In geometry, a triangle is a polygon defined by three sides and three interior angles. The addition of all interior angles within any triangle is always 180 degrees, a fundamental rule known as the angle sum property. Triangles are classified into 6 primary types based on their specific side lengths and angle measurements. Each category possesses unique characteristics. In this article, you will learn about these types of triangles and their distinct geometric properties.  

What are the Different Types of Triangles?

Triangles are among the most ubiquitous geometric shapes in our daily lives, appearing in everything from sandwich halves to warning signs. Due to their inherent rigidity and structural stability, triangles are widely utilized in engineering and construction. They are classified into two primary categories: one based on side lengths and another based on interior angle measurements. 

Types of Triangles Based on Sides

The unique properties of a triangle's side lengths determine its classification. Below, we examine the different types of triangles categorized by their sides.

Types of Triangles Based on Sides

1. Equilateral Triangle

2. Isosceles Triangle

3. Scalene Triangle

1. Equilateral Triangle 

If a triangle has an equal length on all three sides, it is defined as an equilateral triangle. In this shape, the value of each interior angle is exactly 60 degrees. Because all its angles are equal, it is also referred to as an equiangular triangle. An illustration of an equilateral triangle is provided below.

2. Isosceles Triangle 

A triangle with two equal sides is called an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal. Simply put, an isosceles triangle features 2 congruent sides and 2 congruent angles. Both the equilateral and isosceles types of triangles exhibit reflection symmetry. An illustration of an isosceles triangle is provided below. 

3. Scalene Triangle 

When a triangle has three sides of unequal lengths, it is classified as a scalene triangle. In this type of triangle, there are no equal sides and no equal interior angles. An illustration of a scalene triangle is provided below.

Types of Triangles Based on Angles

The specific characteristics of interior angles provide another method for classifying triangles. Below, we discuss the different types of triangles based on their angular properties.

Types of Triangles Based on Angles

1. Acute-angled Triangle

2. Obtuse-angled Triangle

3. Right-angled Triangle

1. Acute-angled Triangle 

If a triangle has three acute interior angles, each measuring less than 90 degrees, it is known as an acute-angled triangle. An illustration of an acute-angled triangle is provided below.

2. Obtuse-angled Triangle 

If a triangle contains one obtuse angle—meaning an angle greater than 90 degrees—it is classified as an obtuse-angled triangle. An illustration of an obtuse-angled triangle is provided below.

3. Right-angled Triangle 

If a triangle contains one right angle, measuring exactly 90 degrees, it is called a right triangle. In this configuration, the side opposite the 90-degree angle is the longest side, known as the hypotenuse, while the other two sides are shorter. An illustration of a right triangle is provided below.

You will frequently encounter combined classifications, such as a right isosceles triangle, which describes a triangle possessing two equal sides, two equal angles, and one 90-degree angle.