Curriculum  /  Math  /  8th Grade  /  Unit 3: Transformations and Angle Relationships  /  Lesson 10

Transformations and Angle Relationships

Lesson 10

Math

Unit 3

8th Grade

Lesson 10 of 22

Objective

Review rigid transformations and congruence between two figures.

Common Core Standards

Core Standards

  • 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

  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

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.

Lesson Materials

  • Optional: Patty paper (transparency paper)

Problem Set

15-20 minutes

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

Target Task

5-10 minutes

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

a.   Which of the four figures are congruent to Figure 1?

b.   For two of those figures identified in part (a), describe a sequence that proves the congruency between Figure 1 and the other figure.

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.

  • Activity: Students create their own transformation sequences on graph paper and then swap with another student who describes/writes the sequence, and vice versa
  • MARS Summative Assessment Tasks for Middle School Aaron's Designs — After this problem, students could create their own designs using transformations
  • Illustrative Mathematics Point Reflection
  • Desmos Transformation Golf: Rigid Motion — This 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 Transformations — A 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 Diagonal — Challenge
  • Khan Academy Geometric Transformations — This 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.

Next

Define a dilation as a non-rigid transformation, and understand the impact of scale factor.

Lesson 11
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Lesson Map

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Topic A: Congruence and Rigid Transformations

Topic B: Similarity and Dilations

Topic C: Angle Relationships

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