Isosceles Right Triangle

An isosceles right triangle is a right triangle with the two legs (and their corresponding angles) equal. An isosceles right triangle therefore has angles of , , and . For an isosceles right triangle with equal legs of length , the hypotenuse has length . The hypotenuse length for is called Pythagoras's constant.

Polyforms made up of isosceles right triangles are called polyaboloes.

The altitude from the right angle to the hypotenuse of an isosceles right triangle with equal legs of length is

(1)

and the area is

			(2)
			(3)
			(4)
			(5)

where is the inradius and is the circumradius.

The inradius and circumradius are

			(6)
			(7)

Triangle line picking for points in an isosceles right triangle with edge lengths , , and gives a mean line segment length of

			(8)
			(9)
			(10)