doug mitchell ms. reyes 8 th grade class. one of greece‘s first great mathematical thinkers,...

The Pythago What?

Understanding the Pythagorean Theorem

Doug MitchellMs. Reyes 8th Grade Class

PYTH

AG

OR

AS

(57

0 – 4

90

B.C

.) One of Greece‘s first great mathematical thinkers, Pythagoras was also a philosopher with a devoted group of followers called Pythagoreans.

A2

 + B

2 =

C2

Pythagoras's formula is one of the greatest contributions to mathematics in ancient times.

Solving with the Pythagorean TheoremThe Pythagorean Theorem states that:“The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.”

According to the Pythagorean Theorem, the sum of the areas of the two red squares, squares A and B, is equal to the area of the blue square, square C.

Chasing Triangles

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Applying the Pythagorean Theorem in History

The Pythagorean Theorem was used by the Egyptians to build pyramids that are still standing today.

The pyramids have many right triangles so the Pythagorean Theorem can be used to determine the height or the base of the pyramids.

C² B²

A²

Everyday Uses for the Pythagorean Theorem

The Pythagorean Theorem is one of the most important and fundamental theorems in geometry.

Practical uses of the Pythagorean Theorem can be found in navigation, cartography, engineering constructions, and also in finding angles of elevation and depression.

Pythagorean Theorem Examples

Mr. Doug

Applying the Pythagorean TheoremThe theorem can be used on a baseball field todetermine distances. Since the infield is a

squarewith right angles you can use the PythagoreanTheorem to determine the distance from homeplate on a baseball field to second base if youknow the distance from first to second base.

Applying the Pythagorean Theorem The distance between each base is 90 feet. How far does a catcher have to throw the ball from home plate to second base? The hypotenuse is the

distance from home plate to second base

Applying the Pythagorean TheoremFighting Fire with Pythagoras

Suppose a firefighter sets his ladder up 8 ft. away from a house . How long does the ladder need to be if they need to reach a window that is 36 ft. from the ground?

Applying the Pythagorean Theorem

What is the distance between two cities? How far is it from Venice to Milan? We looked at a map and saw the three cities make a right triangle. We know the distance from Venice to Rome is 245 miles and Rome is 300 miles from Milan. We can solve to find the distance between Venice and Milan.

Other Pythagorean Theorem Uses

•Navigating a boat•Finding constellations

•Mapping coordinates on a grid•Framing a stained glass window

•Finding the area of a lot•Building an octagonal playhouse

References Pythagoras (2009). Stanford Encyclopedia of

Philosophy. Retrieved from http://plato.stanford.edu.

The Pythagorean Theorem (n.d.). The University of Georgia, Department of Mathematics, EMT 669. Retrieved from http://jwilson.coe.uga.edu

Pythagoras and the Pythagorean Theorem (2008). Articlebase. Retrieved from http://www.articlesbase.com

Using the Pythagorean Theorem (2000). PBS. Retrieved from http://www.pbs.org.