Pythagorean Theorem

Pythagorean Theorem PowerPoint PPT Presentation


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Pythagorean Theorem: Background. Pythagoras was an ancient Greek PhilosopherHe was well respected by the people of the times, they knew he was a great mind, but the leaders of the time were threatened by him and they prohibited him from doing mathematicsHe had to keep his mathematical work secre

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Pythagorean Theorem

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1. Pythagorean Theorem a2 + b2 = c2

2. Pythagorean Theorem: Background Pythagoras was an ancient Greek Philosopher He was well respected by the people of the times, they knew he was a great mind, but the leaders of the time were threatened by him and they prohibited him from doing mathematics He had to keep his mathematical work secret from the Government, so he chose to write in the sand so that there would be no record of his research.

3. A bit of Pythagorean Philosophy Pythagoras argued that there are three kinds of men, just as there are three classes of strangers who come to the Olympic Games. The lowest consists of those who come to buy and sell, and next above them are those who come to compete. Best of all are those who simply come to look on. Men may be classified accordingly as lovers of wisdom, lovers of honor, and lovers of gain. Pythagoras is credited with discovering the numerical ratios which determine the concordant intervals of the musical scale. He believed that similar to musical intervals, in medicine there are opposites, such as the hot and the cold, the wet and the dry, and it is the business of the physician to produce a proper 'blend' of these in the human body. In a well-known passage of Plato's Phaedo (86 bce) we are told by Simmias that the Pythagoreans held the body to be strung like an instrument to a certain pitch. Pythagoreans believed musical tuning and health are alike.

4. Pythagorean Theorem Developed/perfected by Pythagoras It applies only to right triangles It works for all right triangles The formula is used for finding unknown lengths of a right triangle

5. Pythagorean Theorem First some review

6. Pythagorean Theorem The sides of right triangles are labeled a,b,c a and b are non-hypotenuse sides, -also called the legs Side c is always the hypotenuse -this is the side opposite the 90º angle

7. Pythagorean Theorem The formula for Perimeter of a triangle is: P = a + b + c The formula for Area of a triangle is: A = ½ bh (one half base times height) In a right triangle the two “legs” are the base and the height

8. Pythagorean Theorem Area of a square is side squared (s2)

9. Pythagorean Theorem The three sides of a triangle can be shown as sides of three squares.

10. Pythagorean Theorem

11. Pythagorean Theorem

12. Pythagorean Theorem

13. Pythagorean Theorem

14. Pythagorean Theorem We can solve problems using this formula As long as we know the length of 2 of the sides we can figure out the length of the 3rd side.

15. Pythagorean Theorem We can solve problems using this formula As long as we know the length of 2 of the sides we can figure out the length of the 3rd side.

16. Pythagorean Theorem The next time you see the Pythagorean Theorem on a test like the MCAS, remember Pythagoras, drawing triangles in the sand.

17. THANK YOU!

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