817 Math Blog

Pythagoras

• legs
• hypotenuse
• R.A.T
• Greek
• theorem

The legs of a triangle are called sides A and or B These 2 can be switched around. C on the other hand must be the longest side. A hypotenuse is the longest side of a right triangle, the side opposite the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. R stands for right A stands for angle and the T stands for triangle together it is called the right angle triangle. Greek is Where people live now or did but the letters can be used az zeta and beta.A thorem is a problem that can be be shown or proven the answer.

here are some Videos :D

Pythagoras was a famous Greek mathematician who was famous for his ingenuity, his creativity and the fact that no one really knows if he actually did all that he is known for.

R.A.T it is the abbreviation for right angled triangle
Theorem is a theory
Greek is a culture that Pythagoras was from
Legs are the two shorter parts of a triangle that make up a right angle
Hypotenuse is the longest side of the triangle

do you see the right angle on this triangle, it is 90 degrease and if you add up all of the corners it makes 180 degrease

this is just a basic diagram of the theorem of (A) (B) (C)

now i will show you a square

if you see, there are four right angle making the whole thing equal 360 degrease

And that all I got...I might got errors but its okay.... Peace!!!!....

OH NO! MR.Harbeck has amnesia! What ever will we do??? Its a good thing he left us these word and artifacts!

Hi my name is Camille and I will be your teacher for today! Most of you already know what I'm going to be talking about but to some of you this is NEW information. So if okay so Lets start!

This week we have been learning about the Pythagoras Theorem . We have been given an assignment to help our teacher Mr. Harbeck, remember what he was suppose to teach us.The assignment involves us to understand 4 pictures. But I'll get to that a little bit later. We were also given a list of vocabulary words here they are :

• legs
• hypotenuse
• R.A.T.
• Greek
• theorem

Legs- shorter than the hypotenuse , comes out of the right angle, so each right triangle always has 2 legs.

Hypotenuse- is the largest leg in a right angle, triangle and is always opposite to the right angle.

R.A.T- the word R.A.T is a shorter way of saying right angle triangle.

Greek- some one who has the ethnic background of Greece. or a native or inhabitant of Greece.

Theorem- it is a idea that has been proven true.


This is the artifacts one is a Greek man called Pythagoras, a square, a right angled triangle and a2+b2=c2.

First we will be discussing the right angled triangle or also known as R.A.T.
Here is what a right angled triangle looks like:
















A right angled triangle has 3 sides: side A which is the long side on the left and side B which is just under the box also know as 90. then their is side C which is also referred to as the Hypotenuse. The Hypotenuse or C is always the longest side on a R.A.T
Here is a square:

















A square has four equal sides. All 90•.

Another artifact that was found was a formula related to the Right Angle Triangle, that Pythagoras mad. It looks like this :









PYTHAGORAS! This is the Greek Dude we have been learning about!


















Pythagoras was a great mathematician. He is know for the therm, he made - the Pythagoras therm .

~ an interesting fact about Pythagoras was that some people did not believe he was a real person, that the Pythagoras therm was made by a group of people called the Pythagorean.

Pythagoras questions:
Problem 1 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? To answer this question we first need to write what were already know:
we know that 225 cm2 is the area of the square and that all the legs are even.
So first we find out what the square root is for 225 cm is.
it equals to 15cm
So now we know all of the legs or sides equal to 15cm.
Now we need to solve for the Hypotenuse: so we use the Pythagoras therm which we were talking about before.
a2+b2=c2
so if we were to put in the numbers it would look like this:
(15x15)+(15x15)=c2
225+225=c2
450=c2
450 square root is 21.213

(15x4)+(21.213x4)
60+84.852=144.852cm


Word Problem 2
A) The square's diagonal is 4.2 cm.
each square is 3x3 so we use a2+b2=c2
3(squared) + 3(squared) = C2
9+9=c2
18=c2
18[square root] = 4.2 cm

b) the length of the hypotenuse is
the square has 64 squares, 64 divided by 4(sides) is 16
so the square is 16x16, from there we use a2+b2=c2
16(squared)+16(squared)=c2
256+256=c2
512=c2
(square root 512)
22.627 = c
22.627 cm2













OUR VIDEO!!!! :P





















Here is part DEUX !!

An "uber" smart mathematician. Pythagoras was a philosopher from Greek. They say that he was the greatest genius whoever lived. But they weren't sure if he actually existed because there was no trace of him being alive.

Triangle

Square

Pythagorean Theorem is the sum of the areas of the two
squares on the legs A & B which equals the area of the
square on the hypotenuse C.

definitions:

Pythagoras: The greatest genius ever lived. He is a "uber" smart mathematician, he was a Greek geek. It wasn't for sure that he was really alive or even existed.

Legs: These are connected to create the right angle of the right angle triangle a.k.a sides "A" and "B". They are also smaller than the hypotenuse.

Hypotenuse: The hypotenuse is the longest side of the right angle triangle, its the opposite side of the right angle also.

R.A.T: stands for Right Angle Triangle.

Greek : A person thatfrom ancient modern Greece.

Theorem: A theoretical proposition, statement, or formula, something to be proved from other formulas.

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...