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The Pythagorean Theorem

The Pythagorean Theorem. By: Coach McCullers. One of the most influential theorems in Geometry!. Pythagoras: Brief History. Led a Italian society, half religious and half science, which was based on secrecy. Pythagoras believed: that at its deepest level, reality is mathematical in nature,

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The Pythagorean Theorem

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  1. ThePythagorean Theorem By: Coach McCullers One of the most influential theorems in Geometry!

  2. Pythagoras: Brief History • Led a Italian society, half religious and half science, which was based on secrecy. Pythagoras believed: • that at its deepest level, reality is mathematical in nature, • that philosophy can be used for spiritual purification, • that the soul can rise to union with the divine, • that certain symbols have a mystical significance, and • that all brothers of the order should observe strict loyalty and secrecy. • Because of the secrecy, no writings or examples of his work exist. What we know about him comes from what others wrote about him.

  3. Pythagoras: Brief History • He was interested in the principals of mathematics: • The concept of number • The concept of a triangle or other mathematical figures • The abstract idea of proof • The theorem, which bears his name, appears in other early mathematician’s writings.

  4. What is the Pythagorean Theorem? • “The square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs.” • In symbol notation, we write: a2 + b2 = c2

  5. How to use it... • The longest side of the right triangle is called the hypotenuse (c). The hypotenuse is always located across from the right angle. • “a” and “b” represent the legs of the right triangle. • To use, substitute the known values in the Pythagorean Theorem and solve for the unknown.

  6. Remember: legs a2 + b2 = c2 hypotenuse c a hypotenuse legs b

  7. To Solve... • First write the Pythagorean Theorem. a2 + b2 = c2 hypotenuse c a legs b

  8. Substitute known values... • Substitute in the values. 42 + 32 = c2 • Evaluate the squares. 16 + 9 = c2 • Add. 25 = c2 c 4 ft. 3 ft.

  9. Solve for the missing variable. 25 = c2 • Take the square root of both sides. • Final Answer: c 4 ft. 3 ft.

  10. A Flowchart to Follow... Write the Pythagorean Theorem Substitute in the values you know. Solve for the missing part of the triangle. Thank You, Mr. Pythagoras! CHECK YOUR ANSWER!

  11. Your Turn! • Solve for the missing measurement. 13 ft. 5 ft. b

  12. Answer 13 ft. 5 ft. b

  13. Web References History Links: http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html http://www.cut-the-knot.org/pythagoras/index.shtml http://history.hanover.edu/texts/presoc/pythagor.htm Links for Visual Proofs of the Pythagorean Theorem: http://www.dbai.tuwien.ac.at/proj/pf2html/proofs/pythagoras/pythagoras/pythagoras.html http://www.iusb.edu/~abrown/pyth-dem.html http://www.stats.uwaterloo.ca/%7Ecgsmall/pyth_anim.html http://www.tssi.com/Pythagoras%20Connections.html

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