Transformations and Angle Relationships

Lesson 17

Objective

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

Common Core Standards

Core Standards

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  • 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

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  • 7.G.B.5

Criteria for Success

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

Tips for Teachers

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  • 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 comlex angle relationship diagrams.
  • The following materials are useful for this lesson: patty (transparency) paper, protractors, and graph paper.

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Anchor Problems

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Problem 1

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

  1. What is the relationships between $${{\angle AEC}}$$ and $${\angle DEB}$$?
  2. What is the relationship between $${{\angle AEC}}$$ and $${\angle AED}$$?

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.

  1. Name four pairs of congruent vertical angles.
  2. $$\angle 2$$ and $$\angle 8$$ are congruent. How can you prove this?
  3. Name three other pairs of corresponding angles.

Guiding Questions

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Problem Set

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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.

  • 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).

Target Task

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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.

Mastery Response

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