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.
2. What is Pythagorean Theorem? A2 + B2 = C2 Length of the hypotenuse = Square root of length of two shorter sides squared “In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides.” Hypotenuse = longest side of the triangle
3. Who discovered Pythagorean Theorem? Pythagoras Lived in 500s BC Born in Samos Had followers (Pythagoreans) Followers had strict rules
4. How can you use Pythagorean Theorem? Find the length of the hypotenuse of a right triangle Can be reversed to find length of one of the shorter sides. Computing distance between points on a plane Converting between polar and rectangular coordinates
5. An Example If one side of a triangle is 3 cm, and the other is 4 cm, how long is the last side? A2 + B2 = C2 ? cm 3 cm 4 cm
6. An Example (cont.) A = 3 A2 = 9 B = 4 B2 = 16 9 + 16 = 25 √25 = 5 So C is 5 cm 5 cm 3 cm 4 cm
7. Another Example 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?
8. Another Example (cont.) A = 40 A2 = 1600 B = 60 B2 = 3600 1600 + 3600 = 5200 √5200 = 72” 72” > 68” Yes, the TV would fit with 4” extra.
9. The Last Example 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? 200 m ? m 150 m
10. The Last Example (cont.) A = 150 A2 = 22,500 C = 200 C2 = 40,000 22,500 + B = 40,000 40,000 – 22,500 = 17,500 √17,500 ≈ 132 132 + 150 + 200 = 482 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.
11. Works Cited Gay, 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>.
