The Pythagorean Theorem. Warm Up:  Tell a neighbor which sides of the triangle are the legs and which side is the hypotenuse.

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Presentation transcript:

The Pythagorean Theorem

Warm Up:  Tell a neighbor which sides of the triangle are the legs and which side is the hypotenuse.

So what is the Py-tha-go-re-an Theorem?  You will discover the theorem later.  The theorem deals with right triangles and how their sides relate to each other.  Used:  To find a missing side in a right triangle.  To prove a triangle is a right triangle.

History Lesson!  Pythagoras was born around 590 B.C.  Greek mathematician  Earlier people knew the theorem, however, Pythagoras was formally credited.

Discover the Theorem Yourself!  Draw one leg of the triangle with a length of 4 units down.  Draw the other leg of the triangle with a length of 3 units across.  Connect the two ends. This side is 5 units long.  You’ve formed a right triangle! 3 4 5

Discover the Theorem Yourself…  Extend the 4 unit leg to the left to create a square.  Extend 3 unit leg down to create a square.  Repeat with the 5 unit length.  Find the area of each square.  How do they relate to each other?  Thus… a² + b² = c²

Video  cLtN5c&feature=related cLtN5c&feature=related

Pythagorean Triples Consist of three positive integers a, b, and c, such that: Examples: 3, 4, 5 6, 8,10 6, 8,10 5, 12, 13 5, 12, 13 Video

Is it a right triangle?  10, 25, 26 Does 10² + 25² = 26² ? NO  6, 8, 10 Does 6² + 8² = 10² ? YES

Your turn… Let’s play Pythagorean Memory! Compared to all possible groups of 3 numbers, how many do you think will be Pythagorean Triples?

Puzzle Activity Video

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More Pythagorean Theorem EQ: How is a missing side of a right triangle found?

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Example 3  Mr. Rattay wants to put in an underground sprinkler system at EMMS. A drawing of the system is shown. About how many total feet of water pipe will MMS need to buy?  If piping costs $5.00 per foot, how much is the total coast?

Video Links  Jeopardy Game: play.com/Pythagorean-Theorem- Jeopardy/Pythagorean-Theorem-Jeopardy.htmlhttp:// play.com/Pythagorean-Theorem- Jeopardy/Pythagorean-Theorem-Jeopardy.html  Rap: RHQWE&feature=relatedhttp:// RHQWE&feature=related  Football:  Cowboy’s coach: garrett-says-its-important-for-football-players-to- understand-pythagorean-theorem-video/ garrett-says-its-important-for-football-players-to- understand-pythagorean-theorem-video/