
Right Triangle
right  upright or 'perfect'
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:
a^{2} + b^{2} = h^{2}
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
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