9.1: The Pythagorean Theorem
This activity is intended to supplement Geometry, Chapter 8, Lesson 1.
Problem 1 – Squares on Sides Proof
1. Why is the constructed quadrilateral a square?
2. Record three sets of area measurements you made by dragging points
Square on 
Square on 
Square on 
Sum of squares 

3. What conjecture can you make about the areas of the three squares? Does this relationship always hold when a vertex of
Problem 2 – Inside a Square Proof
4. Prove that constructed quadrilateral
5.
The area of the square
Each of the triangles,
Looking at the areas in the diagram we can conclude that:
Substitute the area expressions (with variables
6. Record three sets of numeric values for








7. Does
8. Does
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