OBJECTIVE:    To explore the sum of the interior angles of a polygon in order to discover if there is a general mathematical relation that can be established.
 
  Before beginning this lesson, please review a few things about Sketchpad:

• 1) Measuring Angles: When trying to calculate the measure of angle, e.g., angle ABC, first highlight point A, then, while holding down the shift key, select point B, then point C. Go to "measure" in the menu and select angle. The measure of the angle you selected will print on the screen.

• 2) Finding the Sum of Angles: After measuring each of the angles you are summing together, highlight the calculations that printed on the screen. Go to "measure" in the menu and select "calculate"--a calculator should appear on your screen. Go to "value" and pick your first angle. Press the "+" key, then select the next angle from "value." Continue in this way until you have selected all the angles you wish to sum. Press enter and the value calculated should print on your screen.

• 3) After Calculating Sum: Select one of the corners of your figure and move it around. Does anything change? What stays the same?

First, find the sum of the angles of a triangle.

Next, find the sum of the angles of a quadrilateral.

Thirdly, find the sum of the angles of a pentagon.

What relation do you see? If you don't notice anything yet...

...find the sum of the angles of a hexagon.

...find the sum of the angles of a heptagon.

And, find the sum of the angles of an octagon.

How's it goin'? Any discoveries? Would you like a hint?