### The Pythagorean Theorem

Friday, February 20, 2009

This week we learned about the Pythagorean Theorem. We were given an assignment where we have to explain what the given artifacts are and how we can use the given vocabulary to explain the artifacts.

Artifacts with the vocabulary explaining it: (The vocabulary is in red)

This is a right angle triangle (R.A.T.). It has one 90° internal angle (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side of the triangle. The other two sides are the legs (catheti) of the triangle.

*Hypotenuse-the longest side of the triangle and the opposite of the right angle.
*legs-shorter than the hypotenuse, comes out of the right angle and each triangle always has two legs.

This is a square. A square has four equal sides and four equal angles (90° angles which means that a square is 360 degrees)
.

This is the formula that Pythagoras made for the right angle triangle.

This is a bust of Pythagoras (father of numbers) a Greek mathematician who is best known for the Pythagorean Theorem. He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy.

*Greek- also known as Hellenes, are a nation and ethnic group native to Greece, Cyprus and neighboring regions who can also be found in a plethora of Omogenia
communities around the world.

*Theorem- is a statement proved on the basis of previously accepted or established statements.

Pythagoras and the Pythagorean theorem is important to grade 8 math because this "guy" and this "theorem" started MATHEMATICS and the study of numbers. It's not important to only us grade 8's, it's important to everyone because math is a very important thing.

Pythagoras Problem:

#1 What is the perimeter of the orange triangle?

Solve:

* First you have to look for leg 2 = b.
* The hypotenuse is 914 and leg 1, a, is 17. ALL YOU HAVE TO DO IS SOLVE, BUT FIRST YOU HAVE TO FIND OUT WHAT THE FORMULA IS. YOU'RE LOOKING FOR THE OTHER LEG, leg 2 = b.

To find the perimeter of the orange triangle you have to...

* To get the perimeter you must add a, b and c.

So the perimeter of the orange triangle is 956 cm.

#2 This diagram shows the game plans for a game designed by Harbeck Toys INC. The board is made up of a square and four identical right triangles. If the central square has an area of 225 square centimeters what is the perimeter of the board game?

* The hypotenuse, c, is already given which is 225 cm squared. Since it's a square and all of the sides are equal you just need to find out the square root of 225 which is 15. Leg 1, a, and leg 2, b, is both 15 because all the sides are equal. To get the hypotenuse, you have to add a squared and b squared to get c squared. So 15 squared plus 15 squared is 450. Now, we have to find the square root of 450 which is 21.213. The hypotenuse, c, is 21.213. Now you have to find out what the perimeter is. To get the perimeter you have to first multiply 15, the legs, by 4 because there are 4 sides/triangles. And you will get 60. Then, multiply 21.213, the hypotenuse, by 4 because there are also 4 sides/triangles. And you will get 84.852. Add them together to get the perimeter. And the answer is 144.852.

The perimeter of the board game is 144.852 cm.

Here are some pictures of what we have been doing last week and this week for Pythagoras:

Here's my Pythagoras video: