Keywords: Right triangle,isosceles right triangle,special right triangle

Common Core Standard G.SRT.6

A triangle with two equal sides, and a ninety degree angle will be a 45 45 90 triangle. Notice the triangle drawn inside a circle is a 45 45 90 because the radii are equal, and there is a 90 degree angle.

45-45-90 Triangle

45 45 90

45 45 90

As the name implies a 45-45-90 triangle has two angle measures of 45 degrees, and one of ninety degrees.

A forty five,forty five, ninety triangle has two equal sides.

The hypotenuse is always the longest side, and is opposite the right angle.

The length of the hypotenuse equals, leg length√2

The length of one leg of a 45-45-90 triangle equals, hypotenuse/√2

A helpful angle to side ratio to remember when working with 45 45 90 triangles is as follows:

45 45 90

x x x√2

The legs opposite the forty five degree angles are equal, and the hypotenuse which is opposite the 90 degree angle, is equal to x√2

You can also write this ratio as 1:1: √2

The formula for finding area equals ½(leg)2

A 45 45 90 triangle is also called an isosceles right triangle

The diagonal of a square creates two 45 45 90 triangles.

Questions answered in this video

If given the hypotenuse how do you find the leg length of a 45 45 90 triangle?

If given the leg length how do you find the hypotenuse of a 45 45 90 triangle?

What shortcuts can I use to find the leg lengths of a special right triangle easily?