In this activity, you will explore the relationship between the three sides of a

right triangle known as the Pythagorean Theorem. To the right is an example

of a right triangle with sides a, b, and c.

Activity #1

Open the applet at

Complete the following and answer the corresponding questions.

  1. Begin by selecting “Go to Puzzle #2.”

Question 1: Look at the two white squares. What is true about the areas of these two squares?

  1. Now fill each white square with the red right triangles and the squares that are found below the white square.

Question 2: What is the area of a red right triangle? What is the area of 4 red right triangles?

Question 3: What is the area of a green square?

Question 4: Now, what is the area of the white square on the left in terms of red right triangles and green squares?

Question 5: What is the area of the little light blue square? What is the area of the bright blue square?

Question 6: Now, what is the area of the white square on the right in terms of red right triangles, light blue squares, and bright blue squares?

Question 7: Write an equation that shows the relationship between the square on the left and the square on the right. Simplify the equation by combining like terms.

Based on your exploration, what is the relationship between the sides of a right triangle?

Question 8: Describe side c of the triangle. Be sure to comment on the length compared to other sides and how it is oriented compared to the angles.

STOP AND COMPARE WITH ANOTHER GROUP.

DO NOT PROCEED TO ACTIVITY #2 UNTIL INSTRUCTED.

Activity #2

Open the Decoder Activity at

You are to complete only 3 of the following clues!

Here are the clues you will complete:

Groups 1-4: Clues 1, 5, 8

Groups 5-8: Clues 2, 4, 7

Groups 9-12: Clues 3, 6, 9

At the website, you will click on the boxes and find the clues you are to complete. Once you solve the clue, check the DECODER GRID and write the letter on the line by your clue. Do not complete any other clues unless instructed to do so. You will complete the other clues during next class.

Once you finish your clues, discuss your solutions with another group who solved the same clues. Focus on the process you used to reach a solution.

_____ Clue 1:

_____ Clue 2:

_____ Clue 3:

_____ Clue 4:

_____ Clue 5:

_____ Clue 6:

_____ Clue 7:

_____ Clue 8:

_____ Clue 9:

What is the secret message?