Special Right Triangles

1. Part 1 45-45-90 triangles

2.  Since there is a relationship between the angles of a triangle and the sides of
a triangle, you will find triangles that follow the same pattern.
 The first pattern we will look at is the 45-45-90 triangle. This triangle is
isosceles so 2 of the sides will be the same. Below is a picture of the pattern
you will see. Make sure you pay attention to which side is across from which
angle.

3.  Your first goal is to find x. If you are given the leg, it is easy. If you are given
the hypotenuse, you have a little work. Let’s start with an easy one.

5. The sides across from both 45 angles
are the same (we call them x) so your
other leg is 3. The hypotenuse will be
the leg times the square root of 2. This
works for every 45-45-90 triangle.

6. Find the missing sides.
Need a hint? The hypotenuse
equals the leg times square root
of 2. Set up an equation and
solve for your leg.

7.  The legs are x and the hypotenuse is 𝑥 2. Since the hypotenuse is 13, we
know: 𝑥 2 = 13. Solve for x by dividing by 2. But remember, you can’t have a
radical in the denominator so you have to rationalize it.