 Lesson plan

# Lesson 15: Adding the Angles in a Triangle

teaches Alabama State Standards 8-25.a.
teaches Alabama State Standards 8-25.
teaches Arizona State Standards 8.G.A.5
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards 8.G.A.5 http://corestandards.org/Math/Content/8/G/A/5
teaches Common Core State Standards 8.G.A.2 http://corestandards.org/Math/Content/8/G/A/2
teaches Georgia State Standards MGSE8.G.5.
teaches Kansas State Standards 8.G.5.
teaches New York State Standards NY-8.G.5.
teaches New York State Standards NY-8.G.2.
teaches Ohio State Standards 8.G.5.
teaches Pennsylvania State Standards CC.2.3.8.A.2.

# Lesson 15: Adding the Angles in a Triangle

In this lesson, the focus is on the interior angles of a triangle. What can we say about the three interior angles of a triangle? Do they have special properties?

The lesson opens with an optional activity looking at different types of triangles with a particular focus on the angle combinations of specific acute, right, and obtuse triangles. After being given a triangle, students form groups of 3 by identifying two other students with a triangle congruent to their own. After collecting some class data on all the triangles and their angles, they find that the sum of the angle measures in all the triangles turns out to be 180 degrees.

In the next activity, students observe that if a straight angle is decomposed into three angles, it appears that the three angles can be used to create a triangle. Together the activities provide evidence of a close connection between three positive numbers adding up to 180 and having a triangle with those three numbers as angle measures.

A new argument is needed to justify this relationship between three angles making a line and three angles being the angles of a triangle. This is the topic of the following lesson.

Lesson overview

• 15.1 Warm-up: Can You Draw It? (10 minutes)
• 15.2 Optional Activity: Find All Three (15 minutes)
• 15.3 Activity: Tear It Up (25 minutes)
• Includes "Are you Ready for More?" extension problem
• Lesson Synthesis
• 15.4 Cool-down: Missing Angle Measures (5 minutes)

Learning goals:

• Comprehend that a straight angle can be decomposed into 3 angles to construct a triangle.
• Justify (orally and in writing) that the sum of angles in a triangle is 180 degrees using properties of rigid motions.

Learning goals (student facing):

• Let’s explore angles in triangles.

Learning targets (student facing):

• If I know two of the angle measures in a triangle, I can find the third angle measure.

Required materials:

• copies of blackline master
• pre-printed slips, cut from copies of the blackline master
• geometry toolkits

Required preparation:

• Print copies of the Tear it Up blackline master.
• Prepare 1 copy for every group of 4 students.
• From the geometry toolkit, students will need scissors.
• If you are doing the optional Find All Three activity, prepare 1 copy of the Find All Three blackline master for every 15 students.
• Cut these up ahead of time.

Glossary:

• straight angle -  A straight angle is an angle that forms a straight line. It measures 180 degrees. • Access the complete Grade 8 glossary.

Standards

• This lesson builds on the standard: CCSS.7.G.A.2MS.7.G.2

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.