Transformations and Angle Relationships

Lesson 17

Math

Unit 3

8th Grade

Lesson 17 of 22

Objective


Define and identify corresponding angles in parallel line diagrams. Review vertical, supplementary, and complementary angle relationships.

Common Core Standards


Core Standards

  • 8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
  • 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.B.5

Criteria for Success


  1. Know angle relationship facts about complementary, supplementary, and vertical angles. 
  2. Argue that vertical angles are congruent using a reflection.
  3. Identify corresponding angles in parallel line diagrams.
  4. Argue that corresponding angles in parallel line diagrams are congruent using translations. 

Tips for Teachers


Students may need to review 7.G.5 before they can fully access this lesson and the lessons to follow in this section. Anchor Problem #1 reviews vertical and supplementary angles, but students may need additional review of other angle relationships from seventh grade. These concepts and vocabulary will support students' problem-solving abilities as they encounter more challenging and complex angle relationship diagrams.

Lesson Materials

  • 180° Protractor (1 per student)
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Anchor Problems


Problem 1

Two lines intersect at the origin, as shown in the coordinate plane below.

a.   What is the relationship between $${{\angle AEC}}$$ and $${\angle DEB}$$? Between $${{\angle AEC}}$$ and $${\angle AED}$$?

b.   Use transformations to show that $${{\angle AEC}}$$ is congruent to $${\angle DEB}$$.

Guiding Questions

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Problem 2

In the diagram below, lines $$a$$ and $$b$$ are parallel. Line $$c$$ is a transversal that cuts through the parallel lines.

a.   Name four pairs of congruent vertical angles.

b.    $$\angle 2$$ and $$\angle 8$$ are congruent. How can you prove this?

c.   Name three other pairs of corresponding angles.

Guiding Questions

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Problem Set

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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, lines $$m$$ and $$n$$ are parallel. Line $$p$$ is a transversal that is perpendicular to lines $$m$$ and $$n$$. Line $$q$$ is another transversal.

If $$\angle 1$$ is $${41°}$$, then what is the measure of $$\angle 2$$? Explain how you determined your answer using appropriate vocabulary.

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.

  • Examples where students find all angles that are equivalent to a given angle measure in a parallel line diagram and explain why (This will include alt interior/exterior angles, but students do not need to name these yet, as this comes in the next lesson).
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Lesson 16

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Lesson 18

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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