The document discusses the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It explains that Pythagoras discovered the theorem in 500 BC and provides examples of how to use it to calculate unknown side lengths of right triangles.

1. Pythagorean TheoremKatrina FrancisMath 7H

2. What is Pythagorean Theorem?A2 + B2 = C2Length of the hypotenuse = Square root of length of two shorter sides squared“In a right angled triangle:the square of the hypotenuse is equal tothe sum of the squares of the other two sides.”Hypotenuse = longest side of the triangle

3. Who discovered Pythagorean Theorem?PythagorasLived in 500s BCBorn in SamosHad followers (Pythagoreans)Followers had strict rules

4. How can you use Pythagorean Theorem?Find the length of the hypotenuse of a right triangleCan be reversed to find length of one of the shorter sides.Computing distance between points on a planeConverting between polar and rectangular coordinates

5. An ExampleIf one side of a triangle is 3 cm, and the other is 4 cm, how long is the last side?A2 + B2 = C2 ? cm3 cm4 cm

6. An Example (cont.)A = 3A2 = 9B = 4B2 = 169 + 16 = 25√25 = 5So C is 5 cm5 cm3 cm4 cm

7. Another ExampleI’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?

8. Another Example (cont.)A = 40A2 = 1600B = 60B2 = 36001600 + 3600 = 5200√5200 = 72”72” > 68”Yes, the TV would fit with 4” extra.

9. The Last ExampleI’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?200 m? m150 m

10. The Last Example (cont.)A = 150A2 = 22,500C = 200C2 = 40,00022,500 + B = 40,00040,000 – 22,500 = 17,500√17,500 ≈ 132132 + 150 + 200 = 482You 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.

11. Works CitedGay, Kathlyn. Science in Ancient Greece. N.p.: n.p., n.d. Print. "Pythagoras." Kidipede. History for Kids!, n.d. Web. 29 Nov. 2010. <http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm>. "Pythagoras of Samos." Greek Island Samos. Votsalakia, n.d. Web. 27 Nov. 2010. <http://votsalakia.net/blog/2008/01/27/pythagoras-of-samos/>. "Pythagoras' Theorem." Mathisfun!N.p., n.d. Web. 2 Dec. 2010. <http://www.mathsisfun.com/pythagoras.htm>."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>.

12. Pictureshttp://dannarhitect.files.wordpress.com/2009/08/pythagoras1.jpg?w=234&h=300http://threes.com/cms/images/stories/history/pythagoras.jpghttp://t0.gstatic.com/images?q=tbn:ANd9GcRl8QVwXIyAZH9SdXYVi9UlNEvee7Dc0vRLuku7muN7ejd6o_0uUA