Transformations and Angle Relationships

Lesson 21

Objective

Define and use the exterior angle theorem for triangles.

Common Core Standards

Core Standards

?

  • 8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Foundational Standards

?

  • 7.G.A.2

  • 7.G.B.5

Criteria for Success

?

  1. Extend line segments of a polygon to see exterior angles.
  2. Know that exterior angles are supplementary to the adjacent interior angle.
  3. Know that exterior angles of a triangle are equal to the sum of the two opposite interior angles.
  4. Use the exterior angle sum theorem and other properties of angles to determine additional angle relationships.

Fishtank Plus

Subscribe to Fishtank Plus to unlock access to additional resources for this lesson, including:

  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package

 

Anchor Problems

?

Problem 1

Triangle $${ABC}$$ has two interior angles that measure $${14^{\circ}}$$ and $${30^{\circ}}$$.

 

  1. What is the measure of the exterior angle marked by $$x$$?
  2. What is the relationship between the value of $$x$$ and the two given interior angles?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 8 Mathematics > Module 2 > Topic C > Lesson 14Teacher Version: Example 1

Grade 8 Mathematics > Module 2 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Triangle $${ABC}$$ has an interior angle that measures $${45^{\circ}}$$ and an exterior angle that measures $${129^{\circ}}$$
What is the measure of the interior angle marked by $$x$$?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 8 Mathematics > Module 2 > Topic C > Lesson 14Teacher Version: Example 4

Grade 8 Mathematics > Module 2 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem Set

?

With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

?

Triangle $${ABC}$$ is shown in the diagram below. Show two different ways that you can determine the measure of $$\angle {ABC}$$.

Mastery Response

?

Create a free account or sign in to view Mastery Response