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9.1: The Pythagorean Theorem

Difficulty Level: At Grade Created by: CK-12

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 A, B, and/or C.

Square on BC¯¯¯¯¯¯¯¯ Square on AC¯¯¯¯¯¯¯¯ Square on AB¯¯¯¯¯¯¯¯ 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 ABC is dragged to a different location?

Problem 2 – Inside a Square Proof

4. Prove that constructed quadrilateral EFGH is a square.

5. ABCD is a square with all sides of length (x+y).

The area of the square ABCD is (x+y)2=x2+2xy+y2

Each of the triangles, EFA, FGD, GHC and HEB, is a right triangle with height x and base y. So, the area of each triangle is 12xy.

EFGH is a square with sides of length z. So the area of EFGH is z2.

Looking at the areas in the diagram we can conclude that:

ABCD=EFA+FGD+GHC+HEB+EFGH

Substitute the area expressions (with variables x, y, and z) into the equation above and simplify.

6. Record three sets of numeric values for HEB.

BE BE2 HB HB2 BE2+HB2 EH EH2

7. Does BE2+HB2=EH2 when E is dragged to a different locations?

8. Does BE2+HB2=EH2 when A or B are dragged to different locations?

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Date Created:
Feb 23, 2012
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Nov 03, 2014
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