Constructions, Proof, and Rigid Motion

Lesson 8

Math

Unit 1

10th Grade

Lesson 8 of 19

Objective


Describe and identify rigid motions.

Common Core Standards


Core Standards

  • G.CO.A.1 — Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
  • G.CO.A.2 — Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
  • 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

  • F.BF.B.3
  • 8.G.A.1
  • 8.G.A.2

Criteria for Success


  1. Describe that rigid motions are ways you can move a figure either on or off a coordinate plane without changing size, shape, angles, or relationship between any of the parts.
  2. Identify the rigid motions as translation, rotation, and reflection. 
  3. Describe corresponding points as points on the image and pre-image that lie on top of one another when appropriate transformations are performed. 
  4. Describe the process of "mapping" one figure onto another by matching corresponding parts. Show this through explorations with patty paper. 
  5. Distinguish between corresponding parts that are congruent and those that are not congruent. Use congruence notation appropriately.

Tips for Teachers


  • Students should be able to estimate translations, reflections, and rotations and make an approximation of parameters based on visual inspection. Focus on common transformations such as a quarter turn rotation being equivalent to 90° rotations. 
  • Patty paper is essential to students' visualizing transformations and testing conjectures. There are many types of patty paper and any will work. Amazon has an example of what to look for.
  • Brain Pop “Transformation” may be helpful to give an overview of understanding of transformations.
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Anchor Problems


Problem 1

What was done to get from $$A$$ to $$A'$$, from $$B$$ to $$B'$$, and from $$C$$ to $$C'$$? Make a conjecture and then test your thinking with patty paper.

Guiding Questions

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Problem 2

Describe the transformation to map figure $$A$$ onto figure $$A'$$.

Guiding Questions

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Target Task


Translate the following figure down one unit and to the right two units. Mark all corresponding parts with appropriate notation and all congruent parts with appropriate notation.

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Lesson 7

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Lesson 9

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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