- Take out a sheet of paper. Put a heading on it with your name, date, and period.

- Copy the table below to the top of your paper:

**# of sides**3 4 5 ... *n***sum of measures of ext. <s**...

- Start GeoGebra by clicking here. (Select
*Geometry*for the view.)

- Remove the grid and axes from view:
`View -> Grid, View -> Axes`

- Place 3 points on the plane as shown below.

- Using the
*Ray through Two Points*tool (see image below), draw a ray from*A*through*B*.

- Now draw rays
*BC*and*CA*.

- Let's add angle measures for the
**exterior angles**of triangle*ABC*. Using the*Angle*tool, click on the lines as shown below to have the first exterior angle measured. Note that you'll probably have to turn off the reflex angle by right-clicking the angle, clicking`Object Properties`, clicking on the`Basic`tab, and unchecking`Allow Reflex Angle`.

- Now add the remaining angle measures.

- On your paper, copy and complete the following:

Sum of the exterior angles for a 3-gon (triangle): measure of ext. < @ A = ______ @ B = ______ + @ C = ______ -------------------------------- ______

**Hint:**Use the Windows calculator to sum the angle measures! Click`Start`,`Run`, type`calc`, and click`OK`.

Write the total in the appropriate place in the table at the top of your paper.

- Right-click on ray
*CA*and delete it.

- Add a fourth point to the plane as shown below.

- Draw rays
*CD*and*DA*as shown below.

- Add the exterior angle measures as shown below. Feel free to move your points around to change the shape of your quadrilateral.

- On your paper, copy and complete the following:

Sum of the exterior angles for a 4-gon (quadrilateral): measure of ext. < @ A = ______ @ B = ______ @ C = ______ + @ D = ______ -------------------------------- ______

Write the total in the appropriate place in the table at the top of your paper.

- Now delete ray
*DA*, add a fifth point to the plane (*E*), draw rays*DE*and*EA*, and add the missing exterior angle measures.

- On your paper, copy and complete the following:

Sum of the exterior angles for a 5-gon (pentagon): measure of ext. < @ A = ______ @ B = ______ @ C = ______ @ D = ______ + @ E = ______ -------------------------------- ______

Write the total in the appropriate place in the table at the top of your paper.

- By now, you should notice a pattern. Write the following statement on your paper and fill in the blank.

**The sum of the exterior <s of any polygon is**`___________________________`.

- Your HW is
**P263, 1-2, 4-6, 8-9**. Click here to get started now!