Pythagoras

Wednesday, February 18, 2009
This week, we were assigned to learn about Pythagoras' theorem. We were given important vocabulary that would help us figure out how these artifacts are linked together.

Hypotenuse - the longer side of the triangle. The hypotenuse is on the opposite side of the right angle.

Legs - are the shorter sides of the triangle.

R.A.T. - Right Angle Triangle.

Theorem - a² + b² = c² is Pythagoras' theorem. A theorem is a demonstrated statement that has been proved or needs to be proven.

Greek - A native or citizen of Greece.

This is Pythagoras. Pythagoras was a Greek mathematician who was uber smart. He lived 2500 years ago and died at the age of 90. He is the one who came up with the theory of a² + b² = c². He is important because his mathematical theories and formulas are still used today.

This shape is a right angle triangle (R.A.T.). The shorter sides are called the legs (
a and b). The longest side, across the right angle, is the hypotenuse. The hypotenuse is c. The formula for a right angle triangle is a² + b² = c². a can either be the vertical line, or the bottom line. The same goes to b.

As you can see, this square has all equal sides because there are lines going through it.Each corner is 90 degrees. The whole square equals to 360 degrees.

All these artifacts are linked together because they prove Pythagoras' theorem.

Problem 1

This is a board game and we need to figure out what the perimeter. To do this, we first have to square root the square because it's equal on all sides. You get 15. As you can see, there are lines going through the triangle. That means its equal and the sides of the square are equal to the legs. So that obviously means that the legs and the sides is 15. Now, we have to figure out the hypotenuse. As we now know, Pythagoras' theorem was a² + b² = c². Like I said earlier, the a or b can be either the vertical line or the bottom line.
The question is now 15² + 15² = c².
² just means a number times itself.
(15x15) + (15x15) = c²
225 + 225 = c²
450 = c²
Then, you have to use square root. After you square root, you end up with 21.213. That is the the answer to c². So, the hypotenuse is 21.213. To know if you are right, the hypotenuse is always the higher than the legs.

Here is me and Sharmayne's video on explaining c² - b² = a². We don't have the video of us doing a² + b² = c² because we accidentally deleted and uploaded the wrong video. But, enjoy!