Curriculum  /  Math  /  10th Grade  /  Unit 1: Constructions, Proof, and Rigid Motion  /  Lesson 19

Constructions, Proof, and Rigid Motion

Lesson 19

Math

Unit 1

10th Grade

Lesson 19 of 19

Objective

Describe rigid motions, or sequences of rigid motions that have the same effect on a figure.

Common Core Standards

Core Standards

  • G.CO.A.5 — Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
  • G.CO.B.6 — Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Foundational Standards

  • 8.G.A.2
  • 8.G.A.4

Criteria for Success

  1. Show and describe that there are some conditions under which a composition (or sequence) of transformations can be described by another, single transformation. 
  2. Explain the characteristics of each transformation in the sequence that mimic a single transformation. 
  3. Describe how reflections and rotations of 180 degrees are related, translations and reflections are related when line segments are parallel to a line of reflection.
  4. Describe the features of a figure where some rigid motions have the same effect and some do not (i.e.: angles and line segments may not have the same set of congruent rigid motions).

Tips for Teachers

  • This lesson only has one anchor problem to allow for additional practice from the unit. 
  • Students should be encouraged to determine a sequence of rigid transformations in the least amount of “steps.” 
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Anchor Problems

25-30 minutes

$${{{\overline{AB}}}}$$ is transformed to map to $${\overline{CD}}$$.

  • Adrian describes the transformation shown using the following sequence: 
    • $${{{\overline{AB}}}}$$ is reflected over the y-axis
    • $${\overline{A'B'}}$$ is reflected over the x-axis
  • Tommy describes the transformation shown using the following transformation: 
    • $${{{\overline{AB}}}}$$ is rotated 180° about the origin in a clockwise direction. 
  • Are both students correct? How do you know?

Guiding Questions

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Target Task

5-10 minutes

A rotation of 180° about the origin and reflections about two axis are equivalent transformations.  

Describe two other sets of equivalent transformations. Provide a diagram to support your reasoning.

Lesson Map

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Topic A: Constructions of Basic Geometric Figures

Topic B: Justification and Proof of Angle Measure

Topic C: Translations of Points, Line Segments, and Angles, and Parallel Line Relationships

Topic D: Reflections and Rotations of Points, Line Segments, and Angles

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