Pythagorean Theorem

Pythagorean TheoremGayle HenryMarch 17, 2015

Text: Pythagorean Theorem - Developers name and date.Image: four right triangle1Pythagoras 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

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

2Background InformationIn 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 lets look at some other triangles to make sure youve got it.90 degrees

First lets build some background information.3First Things FirstDiagram 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 1Equilateral TriangleDiagram 2Isosceles Triangle333443Diagram 3Right Triangle34

Self CheckYour turn. Which of the above figures form right angles? abcde

FormulaGood job! Figures a and e are correct. Now lets 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 a2 + b2 = c2. We are solving for c2. Lets do it! ab34c?

Practice3242?32 + 42 = c29 + 16 = c225 = c225 = c25 = c a2 + b2 = c2 Practice with me. Just follow the formula.

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. Lets try what is familiar. You can go 4 miles east, then 3 miles south, totaling 7 miles.43

You may be wondering, ok, but how does this help me? Lets take a look at the following example.8Now what?But, now that you have practiced the Pythagorean Theorem lets apply what youve 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.435

Baseball DiamondImagine 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 2nd 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 batterhomefirstsecondthirdLets play ballDodgersYankees

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

homefirstsecondthird90 feet90 feet

Baseball Diamondsecondhome90 ft.a290 ft.b2c2a2 + b2 = c2

902 + 902 = c2

8100 + 8100 = c2

16,200 = c2

16,200 = c2

127.27 ft = c

Lets see how you did. Great job!Now, lets get ready for our final activity, mathematicians.

8 feet6 feetX feetLets 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

Final Learning Activity6 feet8 feet?a2 + b2 = c2

62 + 82 = c2

36 + 64 = c2

100 = c2

100 = c2

10 = c

Congratulations! Now youve got it.

I hope that you have enjoyed learning about the Pythagorean TheoremYou did a great job!

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