45-45-90 Triangles                    Page 1 of 5
​Accompanying Resource: Printable Study Guide  

What is a 45-45-90 Triangle?

A 45-45-90 triangle can be formed by cutting a square in half.  This is one of two special types of right triangles (the other is a 30-60-90 triangle, which is half of an equilateral triangle).

​What do you know about a square?  All 4 sides are the same length.  Since a 45-45-90 triangle is half of a square, this means that the two sides that form the 90 degree angle are the same length.

For this reason, a 45-45-90 triangle is often referred to as an isosceles right triangle. If you know one of the legs of a 45-45-90 triangle, the other leg will be the same.
​

Welcome to Kate's Math Lessons!  

Teachers,make sure to check out the study guides and activities.

Example    Find x.

We know that one leg of this 45-45-90 triangle is 7 units long.  The two legs that form the right angle in a 45-45-90 triangle are always the same length.  
This means that x is also 7. 

  1      2      ​3      4      5