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Right triangle
Triangle containing a 90-degree angle / From Wikipedia, the free encyclopedia
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A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1⁄4 turn or 90 degrees).
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The side opposite to the right angle is called the hypotenuse (side in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side
may be identified as the side adjacent to angle
and opposite (or opposed to) angle
while side
is the side adjacent to angle
and opposite angle
Every right triangle is half of a rectangle which has been divided along its diagonal. When the rectangle is a square, its right-triangular half is isosceles, with two congruent sides and two congruent angles. When the rectangle is not a square, its right-triangular half is scalene.
Every triangle whose base is the diameter of a circle and whose apex lies on the circle is a right triangle, with the right angle at the apex and the hypotenuse as the base; conversely, the circumcircle of any right triangle has the hypotenuse as its diameter. This is Thales' theorem.
The legs and hypotenuse of a right triangle satisfy the Pythagorean theorem: the sum of the areas of the squares on two legs is the area of the square on the hypotenuse, If the lengths of all three sides of a right triangle are integers, the triangle is called a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.
The relations between the sides and angles of a right triangle provides one way of defining and understanding trigonometry, the study of the metrical relationships between lengths and angles.