Right Triangle
right - upright or 'perfect'
A triangle where one of its interior angles is a right angle (90 degrees).
Try this Drag the orange dots on each vertex to reshape the triangle. Notice it always remains a right triangle, because the angle ∠ABC is always 90 degrees.
Right triangles figure prominently in various branches of mathematics. For example, trigonometry concerns itself almost exclusively with the properties of right triangles, and the famous Pythagoras Theorem defines the relationship between the three sides of a right triangle:
a2 + b2 = h2
where h  is the length of the hypotenuse
a,b  are the lengths of the the other two sides

Attributes

Hypotenuse The side opposite the right angle. This will always be the longest side of a right triangle.
Sides The two sides that are not the hypotenuse. They are the two sides making up the right angle itself.

Properties

  • A right triangle can also be isosceles if the two sides that include the right angle are equal in length (AB and BC in the figure above)
  • A right triangle can never be equilateral, since the hypotenuse (the side opposite the right angle) is always longer than either of the other two sides.

Constructions

You can construct right triangles with compass and straightedge given various combinations of sides and angles. For a complete list see Constructions - Table of Contents.

Related triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises

COMMON CORE

Math Open Reference now has a Common Core alignment.

See which resources are available on this site for each element of the Common Core standards.

Check it out