### Pythagoras Theorem

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-

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.

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.

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