A right-angled triangle is a triangle in which one of the angles is a right angle.
The side opposite the right-angle is known as the hypotenuse of the triangle.
In a right-angled triangle the lengths of the sides are related via Pythagoras Theorem: with side lengths , , and where is the hypotenuse then the following identity holds:
A useful fact about right-angled triangles is that they can be divided into two isosceles triangles. Mark a point at the midpoint of the hypotenuse and join it to the vertex where the right-angle is located. This splits the triangle into two isosceles triangles.
One way to see this is to complete the triangle to a rectangle. The hypotenuse becomes a diagonal of the rectangle. The other diagonal crosses this hypotenuse at its midpoint, and symmetry shows that the four half-diagonals are all the same length. In the rectangle there are four isosceles triangles and two of them coincide with the original right-angled triangle.