1. Special Right Triangles
*You will be able to find the lengths of sides of special right triangles
And

2. Special right triangles are based on the Concept of Similar Triangles!

3. Special Right Triangles
Leg:Leg:Hypotenuse
Short Leg:Long Leg:Hypotenuse

4. LEGS ARE THE SAME LENGTH
In a triangle…
LEGS ARE THE SAME LENGTH
We will use a reference triangle to set up a proportion then solve.

5. This is our reference triangle for the 45-45-90.
Right Triangle 1 1
This is our reference triangle for the

6. EX: 1 Solve for x
Let’s set up a proportion by using our reference triangle. x 3 1 3 x 3 1 1

7. EX: 2 Solve for x x 5 1 5 x 5 1 1

8. EX: 3 Solve for x x 3 45 3 1 1 1 x

10. We will use a reference triangle to set up a proportion then solve.
Right Triangle 60 2 1 30
This is our reference triangle for the triangle.
We will use a reference triangle to set up a proportion then solve.

11. Ex: 1 60 8 60 2 x 1 30 30 y y 8 x 8 2 1 2

12. Special Right Triangles
Solve for x
Ex: 2 30 60 2 x 1 24 60 30 24 x 2 1
2x = 24
x = 12

13. Ex: 3 30 60 2 14 1 y 30 60 x 14 y 14 x 2 2 1
2x = 14
x = 7

14. Ex: 4 x 60 2 1 60 30 y 30 x y 1 2
y = 10
x = 5