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A funny for you… 6-3 Pythagorean Theorem Mrs. Spanier Pre-Algebra 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. You may be wondering… How did people who lived in the B.C. era create right triangles? Using rope! 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! 5 4 3 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 Pythagorean Triples Consist of three positive integers a, b, and c, such that: a 2 b2 c 2 32 42 52 Examples: 3, 4, 5 6, 8,10 5, 12, 13 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? More Pythagorean Theorem EQ: How is a missing side of a right triangle found? 11/13/13: Pick ONE to do. Show work! 1. If a = 7 and b = 24, what is c? 25 2. If a = 20 and c = 29, what is b? 21 This is Sheet #4! HW check today! Think-Pair-Share 1. How do you remember directions like north, south, east, and west? 2. How could a map be used to make a “right triangle”? 3. How could a ladder be used to make a “right triangle”? Example 1 Spanville is 40 miles north of Mechanicsburg, and Franktown is 120 miles east of Spanville. How far is a direct drive from Franktown to Mechanicsburg? WS Problem #1 To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond? WS Problem #2 You just picked up a ground ball at 1st base, and you see the other team's player running towards 3rd base. How far do you have to throw the ball to get it from 1st base to 3rd base to throw the runner out? 90 feet 90 feet Example 3 Mr. Yohn wants to put an underground sprinkler system at MMS. 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: http://www.mathplay.com/Pythagorean-TheoremJeopardy/Pythagorean-Theorem-Jeopardy.html Rap: http://www.youtube.com/watch?v=DRRVuRHQWE&feature=related Football: http://nbclearn.com/nfl/cuecard/51220 Cowboy’s coach: http://nesn.com/2013/07/jason-garrett-says-itsimportant-for-football-players-to-understandpythagorean-theorem-video/