Assignment 1

The goal of this assignment is for students to become familiar with the Pythagorean Theorem using geometry, algebra, and trigonometry. 

Part 1:
Consider a right triangle with a=12 and c=13.  What is the length of b?

How did you find b?  Can you think of a way to show how you found b?

Part 2:
Consider the following two groups of shapes:
4 right triangles with legs of 12 and x
1 square with side length x
1 square with side length 12

4 right triangles with legs of 12 and x
1 square with side length 13

Using the two groups, can you create two squares?
Do these squares have equal areas?
Why does this show that x^2+12^2=13^2?

Assignment:
Make comments below about the steps or methods you went through in each of Part 1 and 2.  What methods did you consider using to answer the questions?  What difficulties did you have?  Think about if you had to present to the class, how would you explain to a classmate how you found the length of b without the use of Part 2, but rather coming up with your own method of showing how you found b.  Also, consider the methods or difficulties of your classmates and respond if you had a similar experience to theirs, if you can help them, or if you had an experience very different from theirs.