Lesson 15: Adding the Angles in a Triangle
Let’s explore angles in triangles.
Illustrative Math Unit 8.1, Lesson 14 (printable worksheets)
Lesson 15 Summary
The following diagrams show how the sum of angles in a triangle is 180 degrees.
Lesson 15.1 Can You Draw It?
- 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.
- Share your drawings with a partner. Discuss your thinking. If you disagree, work to reach an agreement.
Lesson 15.2 Find All Three
Your teacher will give you a card with a picture of a triangle.
- The measurement of one of the angles is labeled. Mentally estimate the measures of the other two angles.
- 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.
- Enter the three angle measures for your triangle on the table your teacher has posted.
Lesson 15.3 Tear It Up
Your teacher will give you a page with three sets of angles and a blank space. Cut out each set of three angles. Can you make a triangle from each set that has these same three angles?
Are you ready for more?
- Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice?
- Repeat this for several more quadrilaterals. Do you have a conjecture about the angles?
Lesson 15 Practice Problems
- In triangle ABC, the measure of angle A is 40°.
a. Give possible measures for angles B and C if triangle ABC is isosceles.
b. Give possible measures for angles B and C if triangle ABC is right.
- For each set of angles, decide if there is a triangle whose angles have these measures in degrees:
a. 60, 60, 60
b. 90, 90, 45
c. 30, 40, 50
d. 90, 45, 45
e. 120, 30, 30
If you get stuck, consider making a line segment. Then use a protractor to measure angles with the first two angle measures.
- Angle A in triangle ABC is obtuse. Can angle B or angle C be obtuse? Explain your reasoning.
- For each pair of polygons, describe the transformation that could be applied to Polygon A to get Polygon B.
- On the grid, draw a scaled copy of quadrilateral ABCD using a scale factor of 1/2.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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