Pythagoras was a Greek mathematician who lived around 2500 years ago. He founded a secretive scientific and religious society in southern Italy. Pythagoras discovered that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs, which is known as the Pythagorean theorem. The Egyptians had previously used this relationship, without realizing it was a mathematical rule, by recognizing that the sides of a 3-4-5 triangle formed a right angle.

1. Measurement Pythagorean Relationship

2. Who was Pythagoras? Why all the fuss about some dead Greek guy? (585 or 565 - 500 B.C.)

3. It all started with the Pyramids! A couple thousand years before Pythagoras, the Egyptians used a unique method to make sure the base of each pyramid was square.

4. How NOT to build a pyramid…

5. Measuring a square corner using a …ROPE?? The Egyptian engineers used a rope tied together at the ends with 12 knots tied in equal distances around the rope.

6. Measuring a square corner using a …ROPE?? They knew that when the rope was shaped into a triangle with sides of 3, 4, and 5 it created a right angle between the sides of 3 and 4. 3 4 5

7. Important term… In a right angle triangle, the side of the triangle opposite the right angle is called the hypotenuse . hypotenuse legs

8. Activity You will work in pairs… You will need… centimetre grid paper scissors Concept Development Page 246, Questions 1-2

9. So…who was Pythagoras? Greek – described as the first pure mathemetician Lived ~ 2500 years ago… Led a secretive society, half scientific and half religious, that he founded in what is now southern Italy

10. Pythagorean relationship hypotenuse legs In a right triangle, the sum of the squares (area) of the legs is equal to the square (area) of the hypotenuse.

11. Pythagorean relationship a 2 + b 2 = c 2 a c b b Area = b 2 Area = a 2 a c Area = c 2

12. Assignment Handout sheet Page 482, Questions 1,2,4,5,6,7

13. Pythagorean theorem