Pythagorean Theorem

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Pythagoras
We were given a assignment on Pythagoras.We had explain who he was. We were given an assignment on Pythagoras. We had explained who he was. Today I will be explaining who Pythagoras is.Pythagoras was a Greek mathematician who was born between 580 and 572 BC, and died between 500 and 490 BC.Pythagoras was the father of mathematics, geometry, music (specifically harmonics), philosophy and medicine. Pythagoras was also the first to start being a vegan because he thought that all animals were his friends that had passed on, also he was the first to say that the earth was a sphere not a square and that the earth was tilted on a axis which was why there were 4 seasons. Pythagoras was also the founding father of the west.




How these Artifacts are linked.

Artifacts:
Right Triangle
Square
a²+b²=c²
Mystery man

1.The artifacts are all related to Pythagoras the Mystery Man.
( The picture) ------------------------------------------------------->
They are also all part of his theorem, the Pythagorean Theorem.






2.
Vocabulary:

Legs- The legs are the opposite of the hypotenuse.----->

Hypotenuse- Its the longest side of a right triangle.----->

R.A.T- Stands for Right Angle Triangle.------------->

Greek- Pythagoras was Greek

Theorem- a formula or a theorem it can be both, a²+b²=c². A Theorem is a statement that proves how they figured out what they were doing.



3. Right
Triangle----------------->
  • All sides equal 180 degrees. Plus theta and beta which equal 90 degrees .
  • It is also calle a R.A.T (Right angle triangle)
  • The opposite side of the right angle is the hypotenuse
  • The opposite side of the hypotenuse is the Legs ( which make up the right angle)
  • The Legs of a right triangle also make up 90




<--- Square-
  • A square is quadrilateral meaning it has 4 sides.
  • There are four 90 degree angles in a square.
  • Half of a square is a triangle.
  • All sides are are the same.



a²+b²=c²- Its the formula for the Pythagorean Theorem.
Which is "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides". --------->
  • A theorem is a idea that has been demonstrated to be true or it is assumed that it would work.
  • Also it is a rule or law made by a formula like the Pythagorean Theorem.




Word Problems

My first problem isn't actually a word problem it with shapes instead of words.


Problem # 1: To solve this problem you need to know how to do the Pythagorean Theorem which is a²+b²=c². Today is will show you how to.

Solution: ( Theorem)
a²+b² = c²
a²+8²-8² = 10²-8²
a²= 10²-8²
a²= (10x10) - (8x8)
a² = 100 - 64
a² = 36
√a² = √36
a = 6





Problem # 2 Now I will show you how do find the perimeter of this board game.
Solution: This is how to solve this question using the Pythagorean Theorem.
a= 15cm- to get 15 you have to √225cm² ( area of the inside square.)
b=15
c=?(21.213)- This is what we are trying to find out.
Theorem:
a²+b² = c²
15²+15² = c²
(15x15) - (15x15) = c²
225 + 225 = c²
450= c²
√450= √c²
21.213 = c
To find the perimeter you need to add up a,b and c 4 times, because that's how many triangles there are.
P=(15+21.123) + (15+21.123)+ (15+21.123)+(15+21.123) = 144.852
P=144.852




If you look below you will find a video on how to solve for A² and also for C².
The reason why i have to different videos is because Mr. Harbeck accidentally deleted ours by mistake (it happens when you have to upload and delete a lot of movies that are either not right or right, you don't know sometimes.)





































Brendan 9-05

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