Pythagoras- Pythagorean Theorem

Wednesday, February 25, 2009
Pythagorean Theorem

Pythagoras

-He was a great Mathematician and Scientist
-He is known for the Pythagorean Theorem (We care because it's math)
-First to think that the Earth was not flat but round
-He discovered square numbers(Square roots)
-He was a Greek Guy
-We don't have any of his work(proof that he was alive)
-Some people say that he didn't exist
-Very smart(I mean very!)



legs
There are two legs in a right triangle. The legs are shorter than the hypotenuse. The legs make the 90 degree angle. The legs are labeled as A or B. It doesn't really matter which leg you label A or B.














Hypotenuse

The hypotenuse is the most important part.The hypotenuse is the longest side of the triangle. The hypotenuse is located opposite of the 90 degree angle. You label it as C.














R.A.T
R.A.T stands for Right Angle Triangle. You can tell if it's a right triangle because the square on the 90 degree angle. A Right Angle Triangle has a total of 180 degree. Two Right Angle Triangles can make a square or a rectangle. The two angles that connect the hypotenuse make 90 degrees.















More about the Pythagorean Theorem...










































This picture is showing the Pythagorean Theorem. It's saying that A2 and B2 will equal the C2.

Squares are important in the Pythagorean Theorem. It will be easier if you know the relationship between a square and a right angle triangle. As you know a square has four equal sides. It has for corners, and those four corners are 90 degree angles. If you have four corners then 90x4=360. then the whole square has an angle of 360. If you cut a square up like you see in the picture, you will get two right angle triangles. And those triangles will contain a 90 degree angle, two equal legs, and a hypotenuse.

Question 1
How do you solve this?
First you label witch side will be A,B, and C. Then look at the information you have. The long line that's 10mm is C so is the other side. It's 10mm. In the inside of the triangle you see a line that is 8mm. That is B. Then on the bottom, we don't know how long it is. We'll call it A. You see that the middle line(B) cuts the triangle in half to make two smaller triangles.We'll solve one side of the triangle first.
C2-B2=A2
lO2-82=C2
(10x10)-(8x8)=C2
100-64=36
36=C
Then you use the square root. The square root of 36 is 6, so 6=A BUT we only solve half of it. You just have to add 6+6 to get 12 because those two sides are the same. It has the line of symmety on A. So The answer for this question is A=12.

Onto question 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 centimetres what is the perimeter of the board game?

Question 2

Well I think that this one is harder than the first. So first lets take 225 and find the square root. The square root is 15 right? To make sure we got it right, we need to check. 225 is the area of the square. To get area you need to times length by with but in this case you need to times side by side. Now our answer was 15. So 15x15=225.
So that means that all the sides of the square is 15. And that also means that the legs for the right triangles are 15 too! now all we need to figure out is the Hypotenuse.

Like for the last question, we need to label. The Hypotenuse is C and the bottom(base) is B and the other one is A.
A2+B2=C2
152+152=C2
(15x15)+(15x15)=450
450=C
Now we need to find the square root of 450. The square of 450 is... 21.213.20344 but we only need 21.213. So the Hypotenuse is 21.213....We are not done yet! The question said that we need to find the perimeter of the board game. So we have to add the sides up.
21.213x4=84.852
15x4= 60
_____________
144.852

So the answer to this question is 144.852.

Here's a video that explains the Pythagorean Theorem(better than I do...)



And...this is the video that I did in class...



1 comments:

  1. Cliff Packman said...

    Couple of interesting extensions to Pythagoras theorem challenges
    https://www.youtube.com/watch?v=YRdKI71tx-4
    and
    https://www.youtube.com/watch?v=li8g0FMD3wc

    March 6, 2015 at 6:43 AM  

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