Teacher Resource Page
Math A

Geometer's Sketchpad Activity

Finding the sum of the interior angles of a polygon.
(Directions for GSP 3.0)

Student Worksheet

Activity 1:

Finding the sum of the interior angles of a polygon.

 

Geometer's Sketchpad Directions:

  1. Set "PREFERENCES" to "Auto-Show Points"
  2. Construct quadrilateral ABCD
  3. Choose a vertex of the quadrilateral and draw all diagonals from that point.
  4. Record the number of triangles formed in a table (such as the one below).
  5. Find the total number of degrees of the interior angles.
  6. Repeat steps 2 - 5 for each polygon listed in the table below.
Name of polygon Number of sides Number of triangles made by diagonal(s) Total number of interior degrees
triangle

3

1

180 degrees
quadrilateral 4    
pentagon 5    
hexagon 6    
septagon 7    
octagon 8    
  9    
  10    
  20    
  n    

Query:  Examine your table.  Can you determine a rule which can be used to predict  the sum of the interior angles of any polygon?  What is it?

 

Activity 2:

Using your prediction (rule), what would be the sum of the interior angles of a decagon?

  1. Under "PREFERENCES" be sure to select "Auto-Show Points" and set the angles to degrees.
  2. Draw a decagon.
  3. Select and measure each angle of the polygon.
  4. Using the calculator tool, compute the sum of these angles.
  5. Does the sum agree or disagree with your prediction?  State why it does or does not agree.

 

Teacher Edition

Sketchpad proficiency level:  Beginner/Intermediate

Sketchpad skills required to complete this activity:

The student should be able to:

  1. Label the vertices of a polygon by setting the preferences.
  2. Construct a line segment.
  3. Construct a polygon.
  4. Construct a diagonal of a polygon using the segment tool.
  5. Use the calculator tool for computational purposes.
  6. Calculate the measure of an angle.

"How-To" Highlights:

1. Construct a Line Segment:
a.  Using the point tool, hold down the shift key and plot 2 points.
b.  Under the CONSTRUCT menu, choose SEGMENT.
2. To Construct a Polygon:
a.  Using the point tool, holding down the shift key and plot points in either a clockwise or counter-clockwise direction.
b.  Select SEGMENT under the CONSTRUCT menu.
3. To Construct a Diagonal:
a.  Using the select tool, hold the shift key down and select 2 non-consecutive vertices.
b.  Under the CONSTRUCT menu, choose SEGMENT.
4. To Use the Calculator:
a.  Select CALCULATOR from the MEASURE menu.
b.  Reminder:  The asterisk (*) is used for multiplication.
5. To Calculate the Measure of an Angle: 
a.  Using the select tool and holding down the shift key, select three consecutive vertices of the polygon.  (Remember the vertex should be selected as the second point.)
b.  Under the MEASURE menu, select ANGLE.
6. To Calculate the Sum of the Angles:
a.  Select CALCULATE from the MEASURE menu.
b.  Select each measurement on the sketch and enter separately into the calculator.
c.  Compute.

This activity was developed by L. Bumpus, J. Galusha, M. Murray and D. Roberts of  Liverpool High School, Liverpool, New York.

 


Murray