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Lesson: Angles in a Triangle
Activity Statement: Can You Draw It?
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.
2. Share your drawings with a partner. Discuss your thinking. If you disagree, work to reach an agreement.
scalene (side
lengths all
di erent)
isosceles (at least
two side lengths
are equal)
equilateral (three
side lengths
equal)
Activity Statement: Find All Three
acute
(all
angles
right
(has a
right
obtuse
(has an
obtuse
acute)
angle)
angle)
Your teacher will give you a card with a picture of a triangle.
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.
Activity Launch: Tear It Up
Activity Statement: Tear It Up
Your teacher will give you and your partner a printed page with three triangles and a blank space.
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 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.
4. Cut out each set of three angles. Can you make a triangle that has these same three angles from each set?
Activity Statement: Missing Angle Measures
In triangle
, the measure of angle
is 50 degrees.
1. Find any two numbers that could be the measures of
and
2. What could be the measures of angles
a. an acute triangle?
is . . .
b. an obtuse triangle?
c. a right triangle?
and
if
in degrees.