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Objectives
 To investigate the sum of the measure of the interior angles of a triangle using
several methods.
 To make a mathematical conjecture from observations.
Materials Needed
 Protractor
 Ruler
 Scissors
 Printout of this activity. Printout of the triangles. Cut out one set of triangles
before you start the activity.
1. Write a definition of a triangle. Include drawings. Clearly show the Interior
Angles and the Exterior Angles. (Note that Interior and Exterior have
different meanings depending on the geometric figure.)
2. Notice that the interior angles of the triangles on your printout are labeled
1, 2, and 3. Cut out one set of triangles. You will be tearing these triangles
into pieces. To keep track of which triangle is A, B, and C, color each
triangle with a different color. Keep the second set of triangles to use later
in the activity.
3. Take triangle A and rip off the angles labeled 1, 2, and 3. Tape the angles
along the lines below so that the angles have common sides. Repeat for
each this for each triangle.
Triangle A
Triangle B
Triangle C
4. What do you notice? Write a conjecture about the sum of the interior
angles of a triangle.
5. Draw (or construct) a line through A parallel to line BC. Label this line with
points D on the left of A and E on the right of A.
6. Trace angle ABC and angle ACB using tracing paper. Compare these
angles to angle DAB and angle EAC respectively. What do you notice?
Can you make a conjecture about the sum of the interior angles of a
triangle from this drawing?
7. Vocabulary: Angles ABC and DAB are called alternate interior angles.
Notice they are congruent!
8. Vocabulary: Angles ACB and EAC are called alternate interior angles.
Notice they are congruent!
9. Next, take a protractor and measure the interior angles of each triangle.
Write the sum of the measurements and use mental math to add the
angles together.
Triangle A ______________________________
Triangle B ______________________________
Triangle C ______________________________
10. What do you notice? What can you conjecture?
11. Using interactive geometry software, set up a triangle. Have the angle
measures showing. Drag point A to several different positions so that you
change the angles of the triangle. Write the sum of the angles for at least
five different triangles. What can you conjecture about the sum of the
interior angles of a triangle from this investigation?
Triangle 1 ______________________________
Triangle 2 ______________________________
Triangle 3 ______________________________
Triangle 4 ______________________________
Triangle 5 ______________________________
12. Do any of the above activities actually prove that the sum of the angles of
a triangle is 180 degrees? Write a summary and a reaction to the different
ways of exploring the angles of a triangle.