## Concept: Triangles

Unit 5 - Pythagorean Theorem

How do you use Pythagorean Theorem and Special Right Triangles to find side lengths of right triangles?

How do you simplify square roots?

## Part One: Working with square roots...

Before you begin learning about Trigonometry and the Pythagorean Theorem, you first must learn how to simplify square roots. To simplify a root, complete these steps. Remember √ = JAIL

1. See if any roots come out even right away (if the number under the root is beyond the parole list, just punch it in

the calculator to see if it is a perfect square).

2. Can you cancel anything? In order to cancel, the numbers need to both be in jail or out of jail.

3. Can you break down any roots? √#on list √# not on list

4. Get rid of any √ in the denominator by multiplying by the same root.

5. GO BACK TO STEP 2!!

REMEMBER: You can't multiply 5√15 but you can multiply √5 √15 because they are both IN JAIL.

1. See if any roots come out even right away (if the number under the root is beyond the parole list, just punch it in

the calculator to see if it is a perfect square).

2. Can you cancel anything? In order to cancel, the numbers need to both be in jail or out of jail.

3. Can you break down any roots? √#on list √# not on list

4. Get rid of any √ in the denominator by multiplying by the same root.

5. GO BACK TO STEP 2!!

REMEMBER: You can't multiply 5√15 but you can multiply √5 √15 because they are both IN JAIL.

PAROLE LIST: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Lesson 1: Simplifying Square Roots

Lesson 2: Simplifying Fractional Roots

Lesson 3: Extra Radical Work

**ALL GEOMETRY**: After you have done the above work, practice solving root equations.

**FOR HONORS:**More Practice with Radical Equations

## Part Two: Pythagorean Theorem: What is it and how is it applied?

To understand the Pythagorean Theorem, watch this video!!

Pythagorean Theorem has many applications. Try these for practice.

Uses of Pythagorean Theorem: Distance Formula

Another Application of Pythagorean Theorem:

There are two special Right Triangles

There are two special Right Triangles

- 45-45-90 triangles and 30-60-90 triangles
- Watch this video before we go through these triangles in class just to give you the basics of what we will learn!!