1. Presentation Lesson Review of Pythagorean Theorem Important vocabulary words are highlighted in red.

2. Theorem: A statement that has been proven to be true based on existing truths. Used mostly in mathematics. Example: In MN, trees bloom in March and April. Based on geographic location of MN and the position of the earth to the sun.

3. Pythagorean Theorem Given a right triangle with sides a and b and hypotenuse c, a 2 + b 2 = c 2. a b c This theorem is attributed to Pythagoras, a Greek mathematician and philospher who lived circa 580’s BCE.

4. Right triangle – a triangle in which one angle is 90 o. The hypotenuse is the side of a triangle with the longest length. 90 o hypotenuse

5. Now do Worksheet B to derive Pythagorean Theorem for yourself.

6. Another way to view the Pythagorean Theorem. Find the area of the inside small square, A small. The length of a side of the big square is 2 and its area is, A big =4. Find x. x s=2 (Mazur, 2003, p.9)

7. A visual of the Pythagorean Theorem. (Wikipedia, 2012).

8. Use the Pythagorean Theorem to solve for the unknown side. 7 5 x

9. 7 5 x

10. 12 5 x (12) 2 + (5) 2 = x 2 144 + 25 = x 2 169 = x 2 x = 13 A Pythagorean triplet has three integers for the lengths of the sides of a triangle. Some examples of triples: (3,4,6) ( 5, 12, 15) (7,24,25) (8,15,17)

11. Now consider the case where the triangle is either a isosceles triangle or an equilateral triangle. An isosceles triangle is a triangle with two sides of equal length. An it’s acute angles are 45 o.

12. An acute angle is angle that is less than 90 o. acute angles

13. The sides of an equilateral triangle all have equal length. Each angle has 60 o.

14. Discussion of isosceles triangle.

15. Discussion of equilateral triangle.

16. Discussion finding the lengths of sides of similar triangles. A similar triangle has the same angles, but may have different lengths of sides. A ratio is the a number that compares the length of one side to another side of a triangle.

17. Sample word problems.

18. References: Wikipedia (2012). Retrieved on 2/24/12 from http://en.wikipedia.org/wiki/Pythagoras. http://en.wikipedia.org/wiki/Pythagoras Mazur, B. (2003). Imaginary Numbers (particularly the square root of minus fifteen). New York: Farrar, Straus and Giroux