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- 1. Pythagorean Theorem<br />Katrina Francis<br />Math 7H<br />
- 2. What is Pythagorean Theorem?<br />A2 + B2 = C2<br />Length of the hypotenuse = Square root of length of two shorter sides squared<br />“In a right angled triangle:<br />the square of the hypotenuse is equal to<br />the sum of the squares of the other two sides.”<br />Hypotenuse = longest side of the triangle<br />
- 3. Who discovered Pythagorean Theorem?<br />Pythagoras<br />Lived in 500s BC<br />Born in Samos<br />Had followers (Pythagoreans)<br />Followers had strict rules<br />
- 4. How can you use Pythagorean Theorem?<br />Find the length of the hypotenuse of a right triangle<br />Can be reversed to find length of one of the shorter sides.<br />Computing distance between points on a plane<br />Converting between polar and rectangular coordinates<br />
- 5. An Example<br />If one side of a triangle is 3 cm, and the other is 4 cm, how long is the last side?<br />A2 + B2 = C2<br /> ? cm<br />3 cm<br />4 cm<br />
- 6. An Example (cont.)<br />A = 3<br />A2 = 9<br />B = 4<br />B2 = 16<br />9 + 16 = 25<br />√25 = 5<br />So C is 5 cm<br />5 cm<br />3 cm<br />4 cm<br />
- 7. Another Example<br />I’m out shopping for an entertainment center. I see a very nice entertainment center on sale. The measurements are 40” by 60”. If my TV was 68” (diagonally), would it fit?<br />
- 8. Another Example (cont.)<br />A = 40<br />A2 = 1600<br />B = 60<br />B2 = 3600<br />1600 + 3600 = 5200<br />√5200 = 72”<br />72” > 68”<br />Yes, the TV would fit with 4” extra.<br />
- 9. The Last Example<br />I’m out trying to get a fence for my yard. The longest side is 200 m. The shorter side is 150 m. How long is the last side?<br />200 m<br />? m<br />150 m<br />
- 10. The Last Example (cont.)<br />A = 150<br />A2 = 22,500<br />C = 200<br />C2 = 40,000<br />22,500 + B = 40,000<br />40,000 – 22,500 = 17,500<br />√17,500 ≈ 132<br />132 + 150 + 200 = 482<br />You would need 483 m of fence, because the square root of 17,500 is actually a little more that so if you only got 482 m, you wouldn’t have enough.<br />
- 11. Works Cited<br />Gay, Kathlyn. Science in Ancient Greece. N.p.: n.p., n.d. Print. <br />"Pythagoras." Kidipede. History for Kids!, n.d. Web. 29 Nov. 2010. <http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm>. <br />"Pythagoras of Samos." Greek Island Samos. Votsalakia, n.d. Web. 27 Nov. 2010. <http://votsalakia.net/blog/2008/01/27/pythagoras-of-samos/>. <br />"Pythagoras' Theorem." Mathisfun!N.p., n.d. Web. 2 Dec. 2010. <http://www.mathsisfun.com/pythagoras.htm>.<br />"The Pythagorean Theorem." Math Forum: Ask Dr.Math. Drexel U., n.d. Web. 29 Nov. 2010. <http://mathforum.org/dr.math/faq/faq.pythagorean.html>. <br />
- 12. Pictures<br />http://dannarhitect.files.wordpress.com/2009/08/pythagoras1.jpg?w=234&h=300<br />http://threes.com/cms/images/stories/history/pythagoras.jpg<br />http://t0.gstatic.com/images?q=tbn:ANd9GcRl8QVwXIyAZH9SdXYVi9UlNEvee7Dc0vRLuku7muN7ejd6o_0uUA<br />

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