Pythagoras Theorem

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We have been learning about the Pythagoras Theorem for about 2 weeks now. I am going to explain what have we learned so far in this lesson.

By the way, here are some words you will need to know throughout this lesson:
Hypotenuse-the opposite side of a right angle and is the longest side which is c.
Legs-the sides of the right angle of 90 degrees
R.A.T-means right angled triangle
Pythagoras-
a mathematician who created this theorem(a^2+b^2=c^2). He lived in Greece and was the first vegetarian. He also thought sound was a medicine that could heal the sick.

Shapes

Square

There are 4 angles that have 90 degrees in this square. In total, it is 360 degrees. So this means this square is quadrilateral.

Right Triangle

R.A.T, Right angled triangle
half of a square
O=theta B=beta
theta and beta are both less than 90 degrees
theta+beta=90 degrees - complementary

Rectangle

There are 4 angles that have 90 degrees, like the square. Which means they can both be quadrilateral.

Right Angle

O=theta B=beta
half of a rectangle
theta and beta are less than 90 degrees
a-leg 1 b-leg 2 c-hypotenuse
c=hypotenuse
(hypotenuse means the longest side)

Here is Pythagoras' theorem:
a^2+b^2=c^2

I will try to help you solve this theorem by showing 2 examples.

So here we are trying to find side a which is the length where the question mark is. 8mm will be side b and 10mm is side c.

a^2+b^2=c^2
a^2+8^2=10^2
-8^2 -8^2
a^2=10^2-8^2
a^2=100-64
a^2=36
Now we try to find the square root of a^2 and 36.
a=6
a+a=|----|
6+6=12mm

Here is the second example:

So here all we know that the area is 225cm^2. We have to try and find the perimeter of the board.

225cm^2=s^2
Now we try and find the square root of 225cm^2 and s^2
15=s
s=legs/a,b
So from this, we can find side a side b and side c by using the theorem.
a^2+b^2=c^2
15^2+15^2=c^2
225=225=c^2
450=c^2
Now all we have to do is find the square root.
21.21=c

So now we know that a=15 b=15 and c=21.21
If we add this all up, we will find the perimeter of the board.

P=(15+15+21.21)+(15+15+21.21)+(15+15+21.21)+(15+15+21.21)
P=51.21+51.21+51.21+51.21
P=204.84
or
P=8(15)+4(21.21)
P=120+84.84
P=204.84

Here is a video of finding side c with the theorem.


Here is another video but finding side a.


That is all for my research about the Pythagoras Theorem. I hoped you learned alot. Thanks, comment.

Leo-73

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