Transformations and Angle Relationships

Lesson 10

Objective

Review rigid transformations and congruence between two figures.

Common Core Standards

Core Standards

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  • 8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.

  • 8.G.A.1.B — Angles are taken to angles of the same measure.

  • 8.G.A.1.C — Parallel lines are taken to parallel lines.

  • 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.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Criteria for Success

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  1. Understand the properties of rigid transformations and their impact on lines, line segments, angle measures, and parallel line relationships. 
  2. Describe a sequence of transformations that demonstrates congruency between two figures.
  3. Perform a sequence of transformations to map one figure to another.
  4. Describe the effects of transformations using coordinate points.

Tips for Teachers

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This can be used as a flex day, depending on the needs of your students. As a result, there are no Anchor Problems. The Problem Set Guidance includes resources, activities, and problem ideas that can be used as a whole class or in small group activities.

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.

  • Activity: Students create their own transformation sequences on graph paper and then swap with another student who describes/writes the sequence, and vice versa
  • Khan Academy Geometric TransformationsThis explores how virtual animation sets are created using geometric transformations. It is a great way to show students how transformations are used in digital arts and give them experience working with transformations online (MP.4). Requires computers.
  • MARS Summative Assessment Tasks for Middle School Aaron's DesignsAfter this problem, students could create their own designs using transformations
  • Illustrative Mathematics Point Reflection
  • Desmos Transformation Golf: Rigid MotionThis is a fantastic activity that allows students to explore transformations using technology; highly recommended. Computers are required.
  • MARS Formative Assessment Lesson for Grade 8 Representing and Combining TransformationsA maze-like activity where students draw connections to different images using transformations. This includes reflections over the lines y=x and y=-x. These can be removed, or students may need additional guidance since these weren't covered in lessons
  • Illustrative Mathematics Reflecting a Rectangle over a DiagonalChallenge

Target Task

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Figure 1 is shown in the coordinate plane below. Four other figures are shown: Figures $${A, B, C,}$$ and $$D$$

  1. Which of the four figures are congruent to Figure 1?
  2. For two of those figures identified in part (a), describe a sequence that proves the congruency between Figure 1 and the other figure.

Mastery Response

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