Transformations and Angle Relationships

Lesson 21

Math

Unit 3

8th Grade

Lesson 21 of 22

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.
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Anchor Problems


Problem 1

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

 

a.   What is the measure of the exterior angle marked by $$x$$?

b.   What is the relationship between the value of $$x$$ and the two given interior angles?

Guiding Questions

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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 Fishtank Learning, 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

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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 Fishtank Learning, Inc.

Problem Set

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Target Task


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

Student Response

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Additional Practice


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

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Lesson 20

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Lesson 22

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Congruence and Rigid Transformations

Topic B: Similarity and Dilations

Topic C: Angle Relationships

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