Pythagorean theorem

Melissa Low
EDU 653
CCSS.Math.Content.8.G.B.6 Explain a proof of the
Pythagorean Theorem and its converse.
Pythagorean Theorem

A long long time ago...
Pythagoras of Samos c.560–480 BC
“was a Greek philosopher and religious leader
who was responsible for important
developments in the history of mathematics,
astronomy, and the theory of music” (PBS)
Around 532 BC he emigrated to Croton. It is said that this was due to
escape Samos’ cruel rule. This may be part of the reason that none of
Pythagoras work has survived (Encyclopedia Britannica).
Pythagoras:
demonstrating his
theorem in the sand

Although, many still have credited
him with his famous proof.
In a right triangle, the square of longest side is
equal to the sum of the square of the other two sides.
Now known as the Pythagorean Theorem
a
b
c
2 2 2
a b c

Important Info about the Pythagorean
Theorem…
 This only works for Right Triangles
 “c” is known as the hypotenuse
 It is the longest side
 It is always across from the right angle
 “a” and “b” are known as the legs of the triangle
 It really does not matter which one we call “a” and which one
we call “b”
a
b
c
2 2 2
a b c

Many have proven the Pythagorean
Theorem since…
Anthony Varela’s Proof
http://www.sophia.org/pythagorean-theorem-
proof/pythagorean-theorem-proof--5-tutorial
Alan Kitching
http://youtu.be/pVo6szYE13Y
Tyler Neylon’s Visual Animation
http://www.youtube.com/watch?v=O0ehw3-FpGg

Emma’s Proof of the Pythagorean Theorem
http://www.youtube.com/watch?v=uOTs2ck1_jU
You will need paper, pencil and a bag of Starburst!
Try Emma’s Proof Yourself…

Now use these cut outs to prove the
Pythagorean Theorem…
 Notice the two squares are the same (7 x 7)
 Cut them out individually
 You should notice also that all the right triangles are
the same. (3 and 4 for the legs)

 Notice, you can cut off 4 triangles on each (purple and
the teal)
 This leaves behind the square (purple) of the long
side on the triangle and the squares of the two legs
(teal). There for they are equal to each other.

Now watch the videos again…
hopefully they make a little bit more
sense.
Alan Kitching
http://youtu.be/pVo6szYE13Y
Tyler Neylon’s Visual Animation
http://www.youtube.com/watch?v=O0ehw3-FpGg

Finding the hypotenuse (longest side of the right triangle
across from the right angle)
It is important to know that
“c” is always across from
the right angle. It does not
matter which one we call a or b.
6
8
?
2 2 2
2 2 2
2
2
2
6 8
36 64
100
100
10
a b c
c
c
c
c
c
Using the Pythagorean Theorem
to find a missing side of a Right Triangle

Using the Pythagorean Theorem
to find a missing side of a Right Triangle
Finding a leg on the right triangle. (one
of the shorter sides of a triangle)
This is still important! “c” is
always across from the right
angle. It does not matter
which one we call a or b.2 2 2
2 2 2
2
2
2
9 15
81 225
-81 -81
144
144
12
a b c
b
b
b
b
b
9
?
15

Now watch this Rap to Help you!
JAKE SCOTT:
The Best Pythagorean Theorem Rap Ever
http://youtu.be/nbopLhP4kpo

D
Using the Pythagorean Theorem to find
distance between two points…
We can use the Pythagorean Theorem
to help us find out how long this line is.
But first we need to draw a right
triangle on our graph using our line
for the hypotenuse.

D
Using the Pythagorean Theorem to find
distance between two points…
Once we have our Right Triangle,
we need to know the side lengths. Which
we see is 10 spaces and 4 spaces.
Now, lets plug it into the Pythagorean
Theorem.
2 2 2
2 2 2
2
2
2
4 10
16 100
116
116
10.77
a b c
c
c
c
c
c

Catch the mistake in this famous
movie!
Clip from the Wizard of Oz
http://youtu.be/kmAxUAh510s
Posted by NASAgeek321

Try this puzzle for fun!
Puzzle File
Created by Bill Lombard, a.k.a. Mr. L:
Teacher & Teacher Trainer;
Conference Presenter;
Print, Web, & Video Author

Sources
"Proving the Pythagorean Theorem." PBS: Public Broadcasting Service. Web. 10
May 2013.
<http://www.pbs.org/teachers/mathline/concepts/historyandmathematics/act1wks
.pdf>.
"Pythagoras: demonstrating his theorem in the sand". Photograph. Encyclopædia
Britannica Online. Web. 10 May. 2013.
<http://www.britannica.com/EBchecked/media/123098/Pythagoras-
demonstrating-his-Pythagorean-theorem-in-the-sand-using-a>.
"Pythagoras". Encyclopædia Britannica. Encyclopædia Britannica Online.
Encyclopædia Britannica Inc., 2013. Web. 10 May. 2013
<http://www.britannica.com/EBchecked/topic/485171/Pythagoras>.

Pythagorean theorem

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