Right Triangles, Acute Triangles and Obtuse Triangles

In this lesson, we will learn how to classify triangles by their angles: Right Triangles, Acute Triangles, Obtuse Triangles.
We can also classify triangles by the lengths of their sides.

A right triangle is a triangle where one of its angles is a right
angle (i.e. 90°). The other two angles are acute angles.

You may have noticed that the side opposite the right angle is
always the triangle's longest side. It is called the hypotenuseof the triangle. The other two
sides are called the legs.

Right triangles are used in many branches of mathematics. For example, in trigonometry and also in the Pythagorean Theorem. The lengths of the sides of a
right triangle are related by the Pythagorean
Theorem. There are also special
right triangles where the sides are of certain fixed ratios.

A right triangle can be isosceles if the two legs are equal in length. A right isosceles triangle will have a 90º angle and two 45º
angles.

A right triangle can not be equilateral because the hypotenuse must always be longer than the legs.

An obtuse triangle has one obtuse
angle (i.e. greater than 90º). The longest side
is always opposite the obtuse angle. In the obtuse triangle shown
below, a is the obtuse angle.

Since the sum of all the angles in a triangle is 180º, only one angle in the triangle can be an obtuse angle , the other two angles must be acute angles.

In this video we discover the six ways to classify trangles, both based on the measure of their side lengths and by the measure of their angles.

The following video illustrates the differences between the acute triangle, the right triangle and the obtuse triangle.

How to classify triangles - acute, obtuse, right

The Three Types of Triangles (Based on What Kinds of Angles They Have)

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