Math 212 EXTRA CREDIT
Winter Term 2009

Laurie Burton's Home Page

Late extra credit assignments will not be accepted

Pythagorean Extra Credit Assignment

You may do any combination of Parts I, II and III.

Part I: 5 points

Go to the BBN Online Learning Center (click here) and find the Math Investigation link in the left gray bar menu. Click on the link and then scroll down to find the 6.4 Math Investigation description and files.

Math Investigation 6.4
Do questions #1 and #2. Turn in actual cut and pasted diagrams with your solution write up. Note that you can download a copy of a GSP (Geometer's Sketchpad) module for Investigation 6.4 into your personal WOU folder from the BBN website. From any WOU terminal server, you can use Programs to open a copy of the GSP program, and then open the downloaded GSP module using the File > Open menu inside GSP. You may be able to complete this investigation using GSP. Feel free to ask for help during office hours.

Note: You can think of the Pythagorean Theorem as Square area + Square area = Square area

Part II: 5 points

Semicircle area + Semicircle area = Semicircle area?
Use Pythagorean triplets to determine the side measures for five different right triangles. Draw them carefully and accurately on graph paper; label the edges and answer the following question

If you draw semicircles on each of the legs and the hypotenuse of a right triangle and compare those areas, what happens?

Note: Semicircle = ½ of a circle, area of a circle is pi x r^2 where r = the radius of a circle.

Part III: 5 points

Triangle area + Triangle area = Triangle area ?
Using the five right triangles from Part II: Redraw the triangles carefully, label the edges and answer the following question:

If you draw equilateral triangles on each of the legs and the hypotenuse of a right triangle and compare those areas, what happens?

Note: All of the angles in an equilateral triangle are 60 degrees. The area of the triangle is ½ x base x height. You will need the Pythagorean Theorem to determine the heights of the equilateral triangles.