1. Pythagorean Theorem
Obj: SWBAT identify and apply the Pythagorean Thm and its converse to find missing sides and prove triangles are right
Standard: M11.C Find the measure of a side of a right triangle using the Pythagorean Thm

2. History of the Pythagorean Thm
At the height of their power, nearly a millennium before Pythagoras, circa BCE , the Babylonians (Babylon located in modern day Iraq) identify what are now called Pythagorean triples (a set of positive integers a, b, c such that a2 + b2 = c2

3. History of the Pythagorean Thm
A Chinese astronomical and mathematical treatise called the Chou Pei Suan Ching (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven, ca B.C.), possibly predating Pythagoras, gives a statement of and geometrical demonstration of the Pythagorean Thm.

4. History of the Pythagorean Thm
Despite evidence predating him, the Greek named Pythagoras is credited with the theorem. According to tradition, Pythagoras once said, “Number rules the universe…” WHAT A FREAKING GENIUS!!!!

5. Basics of the Right Triangle
hypotenuse
leg
leg
Right angle

6. Pythagorean Thm
In ANY right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
a2 + b2 = c2

7. Use the Pythagorean Thm to solve for x.3 4

8. 1. Square both legs 1 2 3 4 5 6 7 8
4 ft 9 10 11 12 13 14 15 16
3 ft
4ft 1 2 3 4 5 6
3 ft 7 8 9

9. 2. Count the total squares1 2 3 4 5 6 7 8
4 ft 9 10 11 12 13 14 15 16
3 ft
4ft 1 2 3
= 25 4 5 6
3 ft 7 8 9

10. 3. Put that number of squares on the hypotenuse2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25
3 ft
4 ft
4ft 1 3 4 5 6 7 8 9 2 10 11 12 13 14 15 16
= 25

11. 4. Count the number of squares that touch the hypotenuse.2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25
3 ft
4 ft
4ft 1 3 4 5 6 7 8 9 2 10 11 12 13 14 15 16
= 25
# = 5

12. 5.That number is the length of the hypotenuse.2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25
3 ft
4 ft
4ft 1 3 4 5 6 7 8 9 2 10 11 12 13 14 15 16
= 25
# = 5
Length = 5

13. WOW, it’s actually the Pythagorean Thm! That’s so freaking cool!!!
LOOK FAMILIAR?!

14. Why are the wrong answers wrong???

15. Pythagorean Triples
Are short cuts! They are sets of 3 whole numbers (a, b, and c) that satisfy the equation a2 + b2 = c2
Most frequent examples:
*** 3, 4, 5 (where a=3, b=4, c=5) ***
5, 12, 13
8, 15, 17
7, 24, 25
ANY scale or multiple of Pythagorean triples will work!!!

16. Pythagorean Triple Example

17. Don’t be fooled by the disguise…
...it’s still the
Pythagorean
Thm!!

18. Pythagorean Thm application with even more Geometry
Pythagorean Thm application with even more Geometry!!! It’s actually that much more fun!!!

19. HOLY SMOKES, LOOK AT ALL OF THIS GEOMETRY!!! A-MAZ-ING!!!!