The Lesson

A right triangle (or a right-angled triangle) is a triangle containing an angle of 90° (called a right angle).

Dictionary Definition

The Oxford English Dictionary defines a right triangle as "a triangle containing a right angle."

The Parts of a Right Triangle

  • A right triangle has one right angle (an angle of 90°). It is shown by drawing a small square.
  • The longest side (opposite the right angle) is called the hypotenuse.
  • The other two shorter sides are called legs or catheti (singular cathetus). They are perpendicular to each other.
  • If another angle is labelled (such as the angle labelled θ in the image below) then we can name the two shorter sides. The side next to the angle is called the adjacent. The side opposite the angle is called the opposite.Note: The adjacent and opposite only exist in relation to an angle. The same side can be an adjacent or an opposite depending on which angle they refer to.

What's in a Name?

A right triangle gets its name from the fact it has a right angle - an angle of 90°. The right triangle is called a right-angled triangle in British English.

The Other Angles in a Right Triangle

The 3 angles in a triangle must add to 180°. If one angle is 90°, the other two angles must add to 90°.

Lesson Slides

The right triangle is one of the most useful triangles in mathematics. It is used for Pythagoras' theorem and in trigonometry. The slider below gives more information about the uses of a right triangle.