Transformations and Angle Relationships

Lesson 20

Math

Unit 3

8th Grade

Lesson 20 of 22

Objective


Define and use the interior angle sum 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. Know that the sum of the interior angles of a triangle is always 180°.
  2. Argue that the sum of the interior angles of a triangle equals 180° by lining the three angles on a straight line.
  3. Use the interior angle sum theorem and parallel line properties of angles to determine additional angle relationships.

Tips for Teachers


Students have experience working with triangles and angle measurements from seventh grade when they investigated unique triangles. While students may know that the angles in a triangle add up to 180°, in this lesson they have the chance to prove this fact using parallel line angle relationships.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems


Problem 1

Lucas is investigating the interior angles of a triangle. He knows that the sum of the angles inside a triangle is $$180{^{\circ}}$$, but he wants to understand why.

He draws a triangle and places it between two parallel lines, with line $$l$$ passing through point $$Q$$ and line $$m$$ passing through points $$P$$ and $$R$$. Explain how Lucas can use his diagram to show $${p+q+r=180}$$.

 

Guiding Questions

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

Problem 2

In the picture below, lines $$l$$ and $$m$$ are parallel. The measure of $$\angle PAX$$ is $${31^{\circ}}$$, and the measure of $$\angle PBY$$ is $${54^{\circ}}$$.

What is the measure of $$\angle APB$$?

 

Guiding Questions

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

References

Illustrative Mathematics Find the Missing Angle

Find the Missing Angle, accessed on Oct. 13, 2017, 4:22 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 3

Determine the angle measures of each interior angle in the triangle.

Guiding Questions

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

Problem Set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


In the diagram below, $$L1$$ is parallel to $$L2$$ and $$L3$$ is parallel to $$L4$$.

a.   What is the measure of ∠5? Show or explain your reasoning.

b.   What other angles have the same measure as ∠5? Show or explain your reasoning.

Student Response

Create a free account or sign in to view Student Response

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.

  • Have students create their own triangle and prove that the sum of the interior angles is 180°.
icon/arrow/right/large copy

Lesson 19

icon/arrow/right/large

Lesson 21

Lesson Map

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

Topic A: Congruence and Rigid Transformations

Topic B: Similarity and Dilations

Topic C: Angle Relationships

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free