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 side lengths
,
the hypotenuse has length 
. The hypotenuse length
for 
is called Pythagoras's constant.
Polyforms made up of isosceles right triangles are called polyaboloes.
The height of area of an isosceles right triangle with side length 
is
 |
(1)
|
and the area is
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
where 
is the height, 
the inradius, and 
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
 |  | ![1/(30)[2+4sqrt(2)+(4+sqrt(2))sinh^(-1)1]a](/images/equations/IsoscelesRightTriangle/Inline36.svg) |
(8)
|
 |  |  |
(9)
|
 |  |  |
(10)
|
