- (5 min) Mental Math
- Take 20% of 200, then add 50 [90]
- Take 1/5 of 45, then subtract 6 [3]
- Take 30% of 80, then multiply by 2 [48]
- If 100% of 60 is 60, what is 400% of 60? [240]
- What is 2/5 of 100? [40]

- (5 min) Review of selected problems from lesson 8 (no more than 3
problems)

- (10 min) Introduce the Pythagorean theorem

Definitions:- A
*right triangle*has one 90 degree angle. - The
*hypotenuse*is the longest side of a right triangle (the one opposite the 90 degree ("right") angle.

The easiest Pythagorean triangle to construct is the [3,4,5] triangle. Draw the squares of the triangle shown (3 ^{2}and 4^{2}) and add them up. You get 25. What is the side of the square whose area is 25?

4^{2}= 16

3^{2}= 9

9 + 16 = 25

Hand out the formulas worksheet, instructing students to put it in their notebook for reference when they do their homework.

Use the equation now, and plug in the following numbers:

Notice that the hypotenuse is always the longest side. Most of the time the numbers do not come out nice. This bothered the Greeks a lot, and they thought that the [3,4,5] triangle was magic. By the way, if you are ever building a house and want to get a right angle, carpenters use the [3,4,5] triangle to construct a right angle.

What if you are given the hypotenuse and only one leg of the triangle? How can you find the missing side, such as in this problem?:

Well, you work the Pythagorean theorem backward, using this formula:

b ^{2}= c^{2}- a^{2}

You find 5^{2}and you subtract 4^{2}to get 3^{2}= 9. then you have to take the square root of your answer (9) to get 3.

- A
- (Remainder of class) In-class exercise

- Hand out homework as students successfully complete the in-class exercise.