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0.3.12 Angles in a Triangle
Lesson Objectives
Observe that the sum of the angles in a triangle is
180 degrees.
Required Materials
geometry toolkits
Setup: Can You Draw It? (5 minutes)
Students in groups of 2. Quiet work time for 3 minutes to complete the table followed by partner and whole
class discussion.
Statement
Anticipated Responses
1. Complete the table by drawing a triangle in each
cell that has the properties listed for its column
and row. If you think you cannot draw a triangle
with those properties, write “impossible” in the
cell.
Answers vary. It is possible to draw all of the triangles
except equilateral right and equilateral obtuse.
2. Share your drawings with a partner. Discuss your
thinking. If you disagree, work to reach an
agreement.
acute
(all
right
(has a
obtuse
(has an
angles
acute)
right
angle)
obtuse
angle)
scalene (side
lengths all
di erent)
isosceles (at least
two side lengths
are equal)
equilateral (three
side lengths
equal)
Setup: Find All Three (10 minutes)
Access to geometry toolkits. Distribute one card to each student, making sure that all three cards have been
distributed for each triangle. Prepare and display a table for all to see with columns Angle 1, Angle 2, Angle 3
and one row for each group of three students.
Statement
Anticipated Responses
Your teacher will give you a card with a picture of a
triangle.
The angle combinations are: 40,50,90; 40,60,80;
50,50,80; 20,20,140; 20,40,120.
1. The measurement of one of the angles is labeled.
Mentally estimate the measures of the other two
angles.
2. Find two other students with triangles congruent
to yours, but with a different angle labeled.
Confirm that the triangles are congruent, that
each card has a different angle labeled, and that
the angle measures make sense.
3. Enter the three angle measures for your triangle
on the table your teacher has posted.
Setup: Tear It Up (20 minutes)
Access to geometry toolkits. Students in groups of 2. Distribute triangle sheet to each group. 5 minutes group
work followed by class discussion. Distribute angle sheet to each group. 5 minutes group work followed by class
discussion.
Statement
Anticipated Responses
Your teacher will give you and your partner a printed
page with three triangles and a blank space.
1. Answers vary. Sample response: None of the
triangles are congruent.
1. Cut the page into two pieces so that one partner
has two triangles and one has a triangle and the
blank space. Together, decide what kind of triangle
to draw in the blank space, and create it. (It should
2. Answers vary. Sample response: The three angles,
when put together to form one angle, appear to
make a line or a 180 degree angle. My partner had
the same result.
look different from the other three triangles.) Are
any of your triangles congruent? Explain how you
know.
2. For each triangle: cut out the triangle, and then
tear off the three corners so that you have three
angles. Line up two of the angles so that two sides
are right next to each other with no gaps, and
their vertices touch. This will create a new, larger
angle. Line up the third angle with this new angle
in the same way. What do you notice about the
place where the three angles come together?
What is the measure of this new angle? How does
your result compare with your partner’s? You and
your partner together should do this for all four
triangles.
Pause for your teacher to check your work.
3. Your teacher will give you a new page. Cut the
page into two pieces so that one partner has two
sets of angles and one has a set of angles and a
blank space. Create a different set of three angles
in the blank space. What is the sum of the
measures of three angles that make a line? Explain
how you know.
3. Answers vary. Sample response:The three angles
measures add up to 180 degrees. I can see this by
looking at a protractor.
4. Answers vary. Sample response:Yes we both were
able to build triangles with different shapes.
4. Cut out each set of three angles. Can you make a
triangle that has these same three angles from
each set?
Setup: Missing Angle Measures (5 minutes)
Cool-down (5 minutes)
In triangle
degrees.
, the measure of angle
Anticipated Responses
is 50
1. Answers vary. Sample responses: 100 and 30, 90
and 40, 80 and 50.
1. Find any two numbers that could be the measures
of and in degrees.
2. What could be the measures of angles
is . . .
a. an acute triangle?
and
if
2. Answers vary. Sample responses: Acute: 80 and 50.
Obtuse: 100 and 30. Right: 90 and 40.
b. an obtuse triangle?
c. a right triangle?
Lesson Summary (5 minutes)
What did you notice about the sum of the angles inside a triangle? Is it possible to make a triangle with any
combination of three angles?