Curriculum  /  Math  /  10th Grade  /  Unit 1: Constructions, Proof, and Rigid Motion  /  Lesson 18

Constructions, Proof, and Rigid Motion

Lesson 18

Math

Unit 1

10th Grade

Lesson 18 of 19

Objective

Describe a sequence of rigid motions that will map a point, line segment, or angle onto another 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. Describe that "mapping" one figure onto another describes the process of performing rigid motions so that each point on the pre-image matches to the corresponding point on the image. 
  2. Identify the predicted transformations necessary to map one figure onto another. 
  3. Verify the sequence of transformations experimentally using patty paper.
  4. Describe the sequence of transformations on a coordinate plane required to map one figure onto another. 
  5. Describe the sequence of transformations off the coordinate plane required to map one figure onto another.

Tips for Teachers

This lesson incorporates figures on the coordinate plane and off the coordinate plane, so a variety of tools can be used to identify, verify, or perform rigid motions. Use the tools that seem most appropriate and in which students need the most practice. 

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Anchor Problems

25-30 minutes

Problem 1

Given line segment $${\overline{AB}}$$, name the coordinates of point A' after the following transformations:

  • Rotation 180° clockwise about the origin. 
  • Translation according to the rule: $${(x,y) \rightarrow (x+2, y-1)}$$

Guiding Questions

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Problem 2

Describe the sequence of transformations that will map $${\angle{EDF}}$$ onto $${\angle {E'D'F'}}$$.

Guiding Questions

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Problem 3

Bob described the sequence of transformations below to map $${{\overline{{EF}}}}$$ to $${{\overline{E'F'}}}$$  

  • Rotate $${{\overline{{EF}}}}$$ about point F, 90° counter clockwise. 
  • Translate $${{\overline{E'F'}}}$$ along vector $${EF}$$. 

  • Show, using patty paper, how you know that the sequence of transformations is incorrect.  
  • Sketch in any references you need to describe a correct sequence of transformations. 
  • Describe a correct sequence of transformations. 

Guiding Questions

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Target Task

5-10 minutes

Below are congruent line segments. Describe a sequence of rigid motions that will map figure $${\overline{AB}}$$ onto $${\overline {A'''B'''}}$$.

Next

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

Lesson 19
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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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