45 / 45 / 90 Triangles

A triangle is a figure that has three sides that meet at points called vertices. Each vertex forms an angle. When added up, all three angles of a triangle equal 180º. Triangles are classified by their angles. A 45/45/90 triangle is a right triangle because one of its angles is 90º.

Right triangles have special properties. All 45/45/90 triangles have the same special properties. In 45/45/90 triangles, the sides opposite of both 45º angles (called legs) are equal to each other since the angles opposite them are equal. So in 45/45/90 triangles, the two sides of the triangle that are equal have a ratio of 1/1.

The length of the longest side of 45/45/90 triangles, hypotenuse, is then length of a leg times√2.

                                         leg times √2

            To sum up all the information about 45/45/90 triangles, one angle is 90º and the other two are 45º. If the length of the legs (the equal sides) is 1x then the length of the longest side is x√2.