12.9 Activity 12V (Proof of the Pythagorean Theorem)
Part A
Rearrange the triangles and squares into the largest square so that they fill it without gaps or overlaps.
After you have completed the rearrangement in Part A, how can you use the additivity principle to easily find the combined area of the pink triangles, blue square, and orange square?
Part B
Rearrange the triangles and square into the larger square so they fill it without any gaps or overlaps.
After you have completed the rearrangement in Part B, how can you use the additivity principle to easily find the combined area of the pink triangles and purple square?
Proof of Pythagorean Theorem
Use Parts A and B and the moving and additivity principles to explain why . (Need a hint? Ask!)
How do we know the places where the triangles and squares meet in our rearrangements really forms a straight line? (Hint: A straight line is .)
Why does this proof tell us about all right triangles? After all, we only used one right triangle to explain the proof.