## Objective

Define and use the exterior angle theorem for triangles.

## Common Core Standards

### Core Standards

The core standards covered in this lesson

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.*### Geometry

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

The foundational standards covered in this lesson

7.G.A.2

### Geometry

7.G.A.2— Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.B.5

### Geometry

7.G.B.5— Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

## Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

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

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## Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

### Problem 1

Triangle$${ABC}$$has two interior angles thatmeasure $${14^{\circ}}$$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 14—Teacher 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 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

### Problem 2

Triangle$${ABC}$$has an interior angle thatmeasures $${45^{\circ}}$$ 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 14—Teacher 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 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

## Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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## Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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

### Student Response

An example response to the Target Task at the level of detail expected of the students.

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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.

- Kuta Software Free Geometry Worksheets
*Congruent Triangles - The Exterior Angle Theorem* - EngageNY Mathematics Grade 8 Mathematics > Module 2 > Topic C > Lesson 14—Teacher Version: Problem Set
- Illustrative Mathematics
*Tile Patterns II: Hexagons*

Lesson 20

Lesson 22