Transformations and Angle Relationships

Lesson 17


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. 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


  • 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


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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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


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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