Concept Byte: The Pythagorean Theorem

Use With Lesson 8-1

ACTIVITY

You will learn the Pythagorean Theorem in Lesson 8-1. The activity below will help you understand why the theorem is true.

Activity

• Step 1 Using graph paper, draw any rectangle and label the width a and the length b.

  

• Step 2 Cut four rectangles with width a and length b from the graph paper. Then cut each rectangle on its diagonal, c, forming eight congruent triangles.

• Step 3 Cut three squares from colored paper, one with sides of length a, one with sides of length b, and one with sides of length c.

  

• Step 4 Separate the 11 pieces into two groups.
  • Group 1: four triangles and the two smaller squares
  • Group 2: four triangles and the largest square
• Step 5 Arrange the pieces of each group to form a square.

1. 1. How do the areas of the two squares you formed in Step 5 compare?
   2. Write an algebraic expression for the area of each of these squares.
   3. What can you conclude about the areas of the three squares you cut from colored paper? Explain.
   4. Repeat the activity using a new rectangle and different a and b values. What do you notice?
2. 1. Express your conclusion as an algebraic equation.
   2. Use a ruler with any rectangle to find actual measures for a, b, and c. Do these measures confirm your equation in part (a)?

3. Explain how the diagram below represents your equation in Question 2.

   

4. Does your equation work for nonright triangles? Explore and explain.

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