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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:


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.


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
Last Modified:
Nov 03, 2014
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