Pythagorean Theorem

Katrina FrancisMath 7H

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 tothe sum of the squares of the other two sides.”• Hypotenuse = longest side of the triangle

Who discovered Pythagorean Theorem?

• Pythagoras• Lived in 500s BC• Born in Samos• Had followers (Pythagoreans)• Followers had strict rules

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

An Example

If one side of a triangle is 3 cm, and the other is 4 cm, how long is the last side?

3 cm

4 cm

? cmA2 + B2 = C2

An Example (cont.)

• A = 3• A2 = 9• B = 4• B2 = 16• 9 + 16 = 25• √25 = 5So C is 5 cm 3

cm

4 cm

5 cm

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?

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.

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?

150 m

200 m

? m

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.

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>.

Pictures

• http://dannarhitect.files.wordpress.com/2009/08/pythagoras1.jpg?w=234&h=300

• http://threes.com/cms/images/stories/history/pythagoras.jpg

• http://t0.gstatic.com/images?q=tbn:ANd9GcRl8QVwXIyAZH9SdXYVi9UlNEvee7Dc0vRLuku7muN7ejd6o_0uUA