1. By Irma Crespo Informal Proof

2. What do you see? ISZBCrespo

3. Meet Pythagoras Known as Pythagoras of Samos. Often described as the first Pure Mathematician. Studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers, perfect numbers etc. Named for his geometric Pythagorean Theorem. ISZBCrespo www.sciencecastle.com http://www.gap-system.org/~history/Biographies/Pythagoras.html

4. Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b). Larson et. al. Geometry. 2001. ISZBCrespo a b c c 2 = a 2 + b 2 hypotenuse leg

5. A Casual Inquiry Informal Proof is a loose style of proof that outlines the main ideas of a formal proof with less detail and more clarity. http://faculty.matcmadison.edu/alehnen/weblogic/logproof.htm#InformalProof It is represented in high level sketches from which formal proofs can be reconstructed. http://en.wikipedia.org/wiki/Proof_theory#Formal_and_informal_proof ISZBCrespo

6. Do the Informal Proof ISZBCrespo

7. The Informal Proof (R. O’Donnell Highlights) Construct the triangle. ISZBCrespo Create two points. Connect the two points to make a line segment. Make the circle. Draw a perpendicular line that intersects the point on the circle. Put a point either above or below the point on the perpendicular line. Connect the points with line segments.

8. The Informal Proof Label the triangle. ISZBCrespo C B A Measure the angles. ABC Measure the segments. ABCBAC

9. The Informal Proof With your angle measurements, do you have a 90 0 angle? What type of triangle do you have? ISZBCrespo With your segment measurements in place, follow the worksheet directions on the computational part to answer each question. Which one demonstrates the Pythagorean Theorem?

10. Create the Equation Group into pairs. Bring out your Pythagoras Square worksheet. Create an algebraic representation of the image on the worksheet following the Pythagorean equation. Explain the connection between the equation and the picture. Write the answers on your own worksheets because these will be graded individually but also jot down the name of your partner on the worksheet. Prepare to explain your answers before the class. After discussion, submit the worksheets for grading. ISZBCrespo

11. Exit Slip ISZBCrespo Write a sentence on how you think Pythagorean Theorem can be applied.

12. Acknowledgement Larson, Boswell, and Stiff. McDougall Littell : Geometry. 2001. ISZBCrespo