Melissa LowEDU 653CCSS.Math.Content.8.G.B.6 Explain a proof of thePythagorean Theorem and its converse.Pythagorean Theorem
A long long time ago...Pythagoras of Samos c.560–480 BC“was a Greek philosopher and religious leaderwho was responsible for importantdevelopments 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 toescape Samos’ cruel rule. This may be part of the reason that none ofPythagoras work has survived (Encyclopedia Britannica).Pythagoras:demonstrating histheorem in the sand
Although, many still have creditedhim with his famous proof.In a right triangle, the square of longest side isequal to the sum of the square of the other two sides.Now known as the Pythagorean Theoremabc2 2 2a b c
Important Info about the PythagoreanTheorem… 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 onewe call “b”abc2 2 2a b c
Many have proven the PythagoreanTheorem since…Anthony Varela’s Proofhttp://www.sophia.org/pythagorean-theorem-proof/pythagorean-theorem-proof--5-tutorialAlan Kitchinghttp://youtu.be/pVo6szYE13YTyler Neylon’s Visual Animationhttp://www.youtube.com/watch?v=O0ehw3-FpGg
Emma’s Proof of the Pythagorean Theoremhttp://www.youtube.com/watch?v=uOTs2ck1_jUYou will need paper, pencil and a bag of Starburst!Try Emma’s Proof Yourself…
Now use these cut outs to prove thePythagorean Theorem… Notice the two squares are the same (7 x 7) Cut them out individually You should notice also that all the right triangles arethe same. (3 and 4 for the legs)
Notice, you can cut off 4 triangles on each (purple andthe teal) This leaves behind the square (purple) of the longside 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 moresense.Alan Kitchinghttp://youtu.be/pVo6szYE13YTyler Neylon’s Visual Animationhttp://www.youtube.com/watch?v=O0ehw3-FpGg
Finding the hypotenuse (longest side of the right triangleacross from the right angle)It is important to know that“c” is always across fromthe right angle. It does notmatter which one we call a or b.68?2 2 22 2 22226 836 6410010010a b ccccccUsing the Pythagorean Theoremto find a missing side of a Right Triangle
Using the Pythagorean Theoremto find a missing side of a Right TriangleFinding a leg on the right triangle. (oneof the shorter sides of a triangle)This is still important! “c” isalways across from the rightangle. It does not matterwhich one we call a or b.2 2 22 2 22229 1581 225-81 -8114414412a b cbbbbb9?15
Now watch this Rap to Help you!JAKE SCOTT:The Best Pythagorean Theorem Rap Everhttp://youtu.be/nbopLhP4kpo
DUsing the Pythagorean Theorem to finddistance between two points…We can use the Pythagorean Theoremto help us find out how long this line is.But first we need to draw a righttriangle on our graph using our linefor the hypotenuse.
DUsing the Pythagorean Theorem to finddistance between two points…Once we have our Right Triangle,we need to know the side lengths. Whichwe see is 10 spaces and 4 spaces.Now, lets plug it into the PythagoreanTheorem.2 2 22 2 22224 1016 10011611610.77a b cccccc
Catch the mistake in this famousmovie!Clip from the Wizard of Ozhttp://youtu.be/kmAxUAh510sPosted by NASAgeek321
Try this puzzle for fun!Puzzle FileCreated 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. 10May 2013.<http://www.pbs.org/teachers/mathline/concepts/historyandmathematics/act1wks.pdf>."Pythagoras: demonstrating his theorem in the sand". Photograph. EncyclopædiaBritannica 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>.