1. 5.1 Special Right Triangles
*You will be able to find the lengths of sides of special right triangles
And

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

3. 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.

4. This is our reference triangle for the 45-45-90.
Right Triangle
This is what we
are given on the EOCT x x
This is our reference triangle for the 1
Here’s how we change it 1

5. Right Triangle x 1 x 1

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

11. Right Triangle
60 2x 2 x 1
30
This is what we’re given on the formula sheet
This is how we change it

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

13. Solve for x
Ex: 2 30 60 2 x 1 24 60 30 24 x 2 1
2x = 24
x = 12

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

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