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Geometer’s Sketchpad Activities
Exploring Geometry
The Exterior Angles of a Triangle
In this activity, you’ll investigate relationships between the interior angles of a triangle and the exterior angles
formed by the rays that extend beyond the triangle’s vertices.
Sketch and Investigate
Use Geometer’s Sketch Pad (GSP) to do the following:
To measure an angle, select
three points making the
vertex the middle selection.
Then from the menu
MEASURE, choose Angle.

Construct a Triangle by drawing 3 rays, so that each ray has an end point that
becomes the vertex of the triangle. Label each of the vertices ABC.

Select the ray, and Construct a point on the ray, then move the point so that it
is outside of the triangle. Do this for each ray, labeling the points D, E, & F.

Use GSP to measure each interior and exterior angle and record their measures
in a data table.
E
Double-Click on the
measured angle to activate
the calculator. Then click
on the measure you want to
use.
C
m ABC = 27°
m CBD = 153°
m BCA = 111°
m ECA = 69°
m CAB = 42°
m FAB = 138°
B
A
D
F

To help you identify patterns and relationships, calculate the sum of any
two of the interior angles. You may do this with a calculator or you may
use GSP to add the measures of angles, by choosing the CALCULATE
option in the menu.
Things to Do . . .
Begin your investigation
Record the initial measured angles on your data sheet, then “Grab” one of the vertex
points of the triangle and relocate it. Record on your data with the new information in
the second row of your table. Continue doing this till you can establish a pattern of
then measures of the angles. Be sure to compare the sum of two interior angles with
an exterior angle.
mABC
mBCA
mCAB
mCBD
mECA
mFAD
Trial 1
Trial 2
Trial 3
Do as many trials as necessary to discover a pattern.
840991236, Created by S. Middleton
1
revised: 05/08/17
From your investigation, you will complete:
1. A Sketch of your initial triangle labeling the points.
2. Your Data Table
3. Your conjecture.
Points to Ponder
In your investigation, you recorded the measures of the interior angles in a triangle,
and you measured the exterior angles FAB, ECA, CBD in a data table. You
also studied the sum of the measures of two of the interior angles in a triangle.
 What do you notice about the relationship between the exterior angle and the
two remote interior angles?
Write a conjecture, about them, and then write a mathematical equation to
express this relationship: ______________________________________

After writing your conjecture, write a mathematical equation using the
symbols and letter of the angles to express the relationship you described in
your conjecture.
(an example of a mathematical equation that would describe a linear pair relationship would
be something like this: CBD  CBA  ABD )

Once you have written both a conjecture and an equation, test them by moving
a point on the triangle again and see if your results confirm your thoughts.
Have Mr. M check your conjecture & Equation before moving on to the next
step.
Going Further & Deeper . . .
Once Mr. M confirms your conjecture, confirm that your conjecture is true for all
of the angles. Do this by writing three mathematical equations. One for each of the
exterior angles and the relationship they have with their remote interior angles.
Then, test these three equations by moving each vertex and doing the calculation
to confirm your conjecture.
840991236, Created by S. Middleton
2
revised: 05/08/17