Geometry is a very broad field of mathematics composed of a wide range of tools that can be used for problem solving. In this module, you are going to research three examples of the implementation of geometry that would employ the use of the Pythagorean Theorem as a problem-solving tool.

The examples you find can come from several different fields of study and applications such as construction, city planning, highway maintenance, art, architecture, and communications, to name a few. The examples you find must clearly demonstrate the use of the Pythagorean Theorem as a tool. Your textbook—Chapter 10, “Modeling with Geometry”—would be a good reference to consult for some examples illustrating the use of the Pythagorean Theorem in applied situations.

For each example you share in your post, address the following:

- Demonstrate the use of the Pythagorean Theorem in the solution of this problem.
- How is the Pythagorean Theorem applied to help solve this problem in this application?
- Why would the Pythagorean Theorem be applied instead of employing some other mathematical tool?
- What tools, unique to this application, would be necessary to get the measurements needed to apply the Pythagorean Theorem?
- Are there other geometrical concepts that are necessary to know in order to solve this problem?
- Are there any modern tools that help solve this kind of problem that either provide a work around, or that rely heavily upon, the Pythagorean Theorem?

When constructing your response, consider the theories, examples, and concepts discussed in your readings this module, and refer to them to support your conclusions.

Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources.

By **Saturday, February 7, 2015**, post your response to the appropriate **Discussion Area**. Through **Wednesday, February 11, 2015**, review the postings of your peers and respond to at least two of them. Consider commenting on the following:

- What other geometrical tools do you feel are necessary to understand in order to solve the examples provided besides the Pythagorean Theorem?
- Do you think we would have the technology that we have today without knowledge of mathematical problem-solving tools such as the Pythagorean Theorem? Explain.