Curriculum  /  Math  /  10th Grade  /  Unit 1: Constructions, Proof, and Rigid Motion  /  Lesson 17

Constructions, Proof, and Rigid Motion

Lesson 17

Math

Unit 1

10th Grade

Lesson 17 of 19

Objective

Use construction and patty paper to rotate a figure not on the coordinate plane. Describe the properties of a rotation.

Common Core Standards

Core Standards

  • 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.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.1
  • 8.G.A.3

Criteria for Success

  1. Verify that a rotation carries segments onto segments of equal length. 
  2. Verify that a rotation carries angles onto angles of equal measure.
  3. Use congruence notation for angles and line segments to note congruent parts. 
  4. Describe that all corresponding parts have the same distance to the point of rotation and same angle measure to the point of rotation. 
  5. Rotate a figure on a coordinate plane given a direction, degree, and center of rotation. Use centers both at the origin and on the figure. 
  6. Locate the center of rotation by determining the perpendicular bisector between corresponding points on the pre-image and the image.
  7. Locate the center of rotation by using corresponding points as points on the rays of an angle, with the vertex of an angle at the rotation point.

Tips for Teachers

Criteria for Success #6 and #7 are beyond the scope of the standards. Students should be exposed to these concepts, but they should not be required for mastery of the topic.

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Anchor Problems

25-30 minutes

Problem 1

Below is a rotation of $${\overline {AB}}$$ to form $${\overline{A'B'}}$$.

What construction steps would you use to transform $${\overline{AB} }$$ to form $${\overline {A'B'}}$$?

 

Guiding Questions

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Problem 2

Transform the figure below according to the rule shown.

$${R_{C,-45Ëš}(\angle{ABD})}$$

Guiding Questions

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Problem 3

Find the center and degree of rotation for the figure below.

Guiding Questions

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Target Task

5-10 minutes

Rotate the following line segment counterclockwise by 45° about center A.

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.

  • Include problems where students need to rotate both line segments and points. 
  • Include error analysis problems where the degree or the direction of rotation is incorrect, and students need to explain why. 
  • Incorporate an introduction to sequences of transformations using a problem that shows two students with two opinions about the transformation to map one figure onto another. Describe who is correct and why. 
  • Include review of other transformations both on and off the coordinate plane. 
  • Include problems where students need to transform a figure by bisecting angles. I.e.: Given a rotation of 60 degrees, show the rotation of 30 degrees.

Next

Describe a sequence of rigid motions that will map a point, line segment, or angle onto another figure.

Lesson 18
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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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