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

Constructions, Proof, and Rigid Motion

Lesson 10

Math

Unit 1

10th Grade

Lesson 10 of 19

Objective

Translate points and line segments not on the coordinate plane using constructions. Describe properties of translations with respect to line segments and angles.

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.4 — Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
  • 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.

Foundational Standards

  • 8.G.A.1
  • 8.G.A.2
  • 8.G.A.3

Criteria for Success

  1. Verify that a translation carries segments onto segments of equal length.
  2. Verify that a translation carries angles onto angles of equal measure.
  3. Use congruence notation for angles and line segments to note congruent parts. 
  4. Use vectors to show direction and magnitude of a translation as well as to construct translations of figures.
  5. Describe the translation using direction and magnitude.
  6. Describe the relationship between translated line segments as parallel.

Tips for Teachers

  • We are not going to be constructing parallel lines as part of this lesson. EngageNY has parallel line construction as part of this lesson, but we are, instead, going to use the properties of distance preservation as the guiding principle for translation. 
  • Notation for Translations is $${T_{\overrightarrow{AB}}(P)}$$.It means that you are translating point P along vector AB. This is notation that students should be familiar with—but you do not need to ensure mastery of this.
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Anchor Problems

25-30 minutes

Problem 1

Estimate where point $$P$$ will be after a translation along vector $${AB}$$.

Guiding Questions

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References

GeoGebra Translation of a Point Along a Vector

Translation of a Point Along a Vector by Match Fishtank is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed Aug. 7, 2017, 2:11 p.m..

Problem 2

Use your compass and straight edge to verify that the translation of $${\overline{AB}}$$ along vector $${CD}$$ results in $${\overline{A'B'}}$$.

Guiding Questions

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Problem 3

Translate the following line segment along vector $${CD}$$ using constructions.

Guiding Questions

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Target Task

5-10 minutes

Translate $${\overline{GH}}$$ using constructions along vector $${EF}$$.
 

Write the algebraic rule for this translation.

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 such as: 
    • Given two translated figures, identify the vector. 
    • Practice constructing the translation on a coordinate plane with a vector and describing how the Pythagorean Theorem can be used to find the length and direction of the vector.
    • “Always sometimes never” problems with properties of translations.

Next

Construct parallel lines. Prove the relationship between corresponding angles. Use this relationship to find missing measures directly and algebraically.

Lesson 11
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

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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