Team: As Easy as ABC
Members: Jenny, Lydia, Aubrey, & Iris
Chapter 12.9 Using the Moving and Additivity Principles to Prove the
Pythagorean Theorem
Class Activity 12Z: A Proof of the Pythagorean Theorem
Pythagorean Theorem:
a2 + b2 = c2
Examples: Solve these triangles using the Pythagorean Theorem.
Proof of the Pythagorean Theorem:
In your group: The following shows a square and triangles. All the triangles shown
are copies of our original right triangle with sides of lengths a, b, and c. The square
shapes have all 4 sides the same length and 4 angles right angles, making them true
squares.
Fill in the bigger square that has the side lengths a + b with triangle and squares
without gaps or overlaps.
Use the following square to draw what you have created.
Now use the moving and additivity principles about areas to explain why
a2 + b2 = c2
(a + b) (a + b) = c2 + 4(½ a + b)