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Triangles (Mathematics Glossary)

What Is a Triangle?

A triangle is a 2-dimensional shape with three sides and three angles.



Dictionary Definition

The Oxford English Dictionary defines a triangle as "a figure (usually, a plane rectilineal figure) having three angles and three sides."

Types of Triangle

There are different types of triangle.

Triangles can be classified by lengths of sides or by angles.

By Lengths of Sides:

Triangles can be classified as equilateral, isosceles or scalene depending on whether 3, 2 or 0 side lengths and angles are equal.



By Angles:

Triangles can be classified as acute, obtuse or right triangles depending on whether all angles are acute (less than 90°), one angle is obtuse (more than 90°) or one angle is a right angle (90°).



Read more about types of triangle

Properties of Triangles

Area of a Triangle

The area of a triangle is found using the formula:



In this formula, b is the length of the base of the triangle and h is the height of the triangle.

Read more about how to find the area of a triangle

Interior Angles of a Triangle

The interior angles of a triangle add up to 180°.



Read more about the interior angles of a triangle

Curriculum
Geometry Lessons
Interactive Test
  show
 


Here's a second test on the triangle.
Here's a third test on the triangle.
Note

What's in a Name?

A triangle has three corners and so three angles. Just as a tricycle has three wheels, and a tripod has three legs, a shape with three angles in called a triangle.

An alternative name for a triangle is a 'trigon', as it is a three-sided polygon. This is where we get the word trigonometry.

Oblique Triangles

A triangle without a right angle is called an oblique triangle.

Acute triangles and obtuse triangles are both oblique triangles.

Finding the Area of a Triangle Using Trigonometry

The standard way to find the area of a triangle is:
½ × base × height
An alternative way to calculate the area of a triangle is using trigonometry.

The area of a triangle is given by the formula:



In this formula, a and b are two sides of the triangle, and C is the angle between these sides.

Read more about how to find the area of a triangle using trigonometry