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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?

Example 1: How to solve a 45 45 90 triangle. What is the length of the hypotenuse of a 45-45-90 triangle with a leg length of 7 units?

Step 1. Use x√(2 )    x = leg length

Step 2. 7√(2 ) units  Identifying 45 45 90 triangles Hypotenuse =
units You may also enjoy  Properties of a special right triangle 45 45 90 Shortcuts for finding 45 45 90 Triangle sides

We all love shortcuts. Try these for finding the side lengths of a 45 45 90 special right triangle.

Just remember √2

Hypotenuse = leg length x √2

Leg length = hypotenuse/√2
45 45 90 Triangles are special right triangles that have unique properties that allow one to find missing angles and side lengths.