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 , , and/or .
Square on | Square on | Square on | Sum of squares |
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3. What conjecture can you make about the areas of the three squares? Does this relationship always hold when a vertex of is dragged to a different location?
Problem 2 – Inside a Square Proof
4. Prove that constructed quadrilateral is a square.
5. is a square with all sides of length .
The area of the square is
Each of the triangles, , , and , is a right triangle with height and base . So, the area of each triangle is .
is a square with sides of length . So the area of is .
Looking at the areas in the diagram we can conclude that:
Substitute the area expressions (with variables , and ) into the equation above and simplify.
6. Record three sets of numeric values for .
7. Does when is dragged to a different locations?
8. Does when or are dragged to different locations?