2. Pythagorean Theorem Gayle Henry March 17, 2015

3. Pythagoras who lived in 500 B.C. was one of the first Greek mathematical thinkers who believed that all things involve numbers. He also believed that mathematics is the basis for everything, and that the physical world can best be understood through mathematics. Pythagorus

4. Background Information In order to use the Pythagorean Theorem you have to start with a right triangle. A right triangle looks like this and measures a 90 degrees angle. In order to find the hypotenuse (longest side) of a triangle this is your starting point. Now let’s look at some other triangles to make sure you’ve got it. 90 degrees

5. First Things First Diagram 1 is an equilateral triangle because all sides are equal. Diagram 2 is an isosceles triangle where only the opposing sides are equal. Diagram 3 is a right triangle where one angle measures 90 degrees. So, when you know the measurement or distance of two angles that make a right angle (diagram 3) you can find the hypotenuse of the remaining side. Diagram 1 Equilateral Triangle Diagram 2 Isosceles Triangle 3 3 3 4 4 3 Diagram 3 Right Triangle 3 4

6. Self Check Your turn. Which of the above figures form right angles? a b c d e

7. Formula Good job! Figures “a” and “e” are correct. Now let’s learn the formula. To find the hypotenuse of a right triangle you have to know the measurement of the two sides that form a right angle in order to solve for “c”. As you can see, the first triangle is labeled a, b, and c. In the second triangle a = 3 and b = 4. The formula is a 2 + b 2 = c 2. We are solving for c 2. Let’s do it! a b 3 4 c ?

8. Practice 3232 4242 ? 3 2 + 4 2 = c 2 9 + 16 = c 2 25 = c 2 √25 = c 2 5 = c a 2 + b 2 = c 2 Practice with me. Just follow the formula.

9. How Does this Help Me? Say you are planning to meet your friends at the museum. They are already there. You need to decide the quickest route to get there. Let’s try what is familiar. You can go 4 miles east, then 3 miles south, totaling 7 miles. 4 3

10. Now what? But, now that you have practiced the Pythagorean Theorem let’s apply what you’ve learned. Instead of traveling 7 miles by going 4 miles east, then 3 miles south, I can travel the shorter distance after applying the Pythagorean Theorem in which 5 = c. 4 3 5

11. Baseball Diamond Imagine your are playing baseball and the bases are loaded. You play second base. Knowing that the bases are right angles, what is the distance between 2 nd base and home in order to get the runner out coming from third base? You may want to use the Pythagorean Theorem to find the hypotenuse from second base to home base to judge the distance of your throw. Here batter batter home firstsecond third Let’s play ball Dodgers Yankees

12. Baseball Diamond The distance from home to 1 st base is 90 feet, 1 st to 2 nd is 90 feet and so on. Now, lets use the Pythagorean Theorem to find the distance of your throw from 2 nd base to home. Please pause while you solve. home firstsecond third 90 feet

13. Baseball Diamond second home 90 ft. a 2 90 ft. b 2 c2c2 a 2 + b 2 = c 2 90 2 + 90 2 = c 2 8100 + 8100 = c 2 16,200 = c 2 √16,200 = c 2 127.27 ft = c Let’s see how you did. Great job! Now, let’s get ready for our final activity, mathematicians.

14. 8 feet 6 feet X feet Let’s help Abby find the distance from the fence to her basket. For example, Abby climbs the 6 feet tall fence. The tree and the ground make a right angle and the basket is 8 feet away. So, how far away is Abby from the basket? Please pause while you solve. 90 degree

15. Final Learning Activity 6 feet 8 feet ? a 2 + b 2 = c 2 6 2 + 8 2 = c 2 36 + 64 = c 2 100 = c 2 √100 = c 2 10 = c Congratulations! Now you’ve got it.

16. I hope that you have enjoyed learning about the Pythagorean Theorem You did a great job!