The Pythagorean Theorem

1. The Pythagorean Theorem By: Fiona Luo and LynelValderama

2. Groups • Group 1: Brooke, Stephie, Ethan S., Nathan, Katie, Aarfa, Ethan K. • Group 2: Jacob, Naz, Max, Ethan H., Tyrel, Katelynn • Group 3: Corey, Carson, Andrew, Sienna, Mavleen, Ben • Group 4: Fynn, Aidan, Selena, Dominique, Ellen, Kyle, Adam

3. What is the Pythagorean Theorem? • A theorem that states the square of the hypotenuse of a right triangle, is the sum of the squares of the legs of that right triangle • Can be written as a simple equation: a2 +b2 =c2

4. Pythagoras • The Pythagorean Theorem was developed by Pythagoras • Pythagoras was born at about 569 BC in Samos, Greece • He died at about 500 BC in Lucainia, Italy • Often referred to as “first pure mathematician” • Created a math group called the Pythagoreans

5. Pythagorean Theorem Proof Using Algebra: Four “abc” triangles in Diagram Area of the entire square… Each side of square has a length of a+b so area equals (a+b)2 [(a+b)(a+b)] Area of the other parts… The area of the smaller square = c2 The area of the one of the four triangles = ½ab *ab/2* (area of a triangle formula) Which means the area of the four triangles combined would be = 4(½ab) = 2ab Then, add area of smaller square to triangles = c2 + 2ab (this is equal to the area of the large square) (a+b)(a+b) = c2 + 2ab Expanded: a2 + 2ab + b2 = c2 + 2ab Subtract: - 2ab - 2ab a2 + b2 = c2 • The Pythagorean Theorem indicates that in a right triangle, a2 + b2 =c2 … To expand (a+b)(a+b), use the FOIL method. Multiply the First terms, Outer terms, Inner terms, and finally, the Last terms.

6. Bonus Questions 10 What are the values of the unknown legs? Round the values to the nearest tenth and show your work. Hint: Find “x” first 

7. References