Exterior Angles Lab in GeoGebra

Mr. Ferraro, Balboa High School


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

  2. Copy the table below to the top of your paper:

    # of sides345 ... n
    sum of measures of ext. <s      ...  


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

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

  5. Place 3 points on the plane as shown below.


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



  7. Now draw rays BC and CA.


  8. 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.



  9. Now add the remaining angle measures.


  10. 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.

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


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


  13. Draw rays CD and DA as shown below.


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



  15. 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.

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



  17. 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.

  18. 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 ___________________________.

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