This document provides information about Pythagoras and the Pythagorean theorem. It discusses how Pythagoras, a Greek philosopher and mathematician, is credited with discovering the theorem around 532 BC. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document then provides several examples and proofs of the theorem, and discusses how it can be used to find missing sides of a right triangle. It concludes by providing a link to a rap video that helps explain the theorem.

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

2. 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

3. 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

4. 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

5. 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…

6. How can we use the Pythagorean Theorem?
Finding the hypotenuse (longest side of
the right triangle)
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
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.
9
?
15
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

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

8. 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>.