Transformations and Angle Relationships

Lesson 13

Math

Unit 3

8th Grade

Lesson 13 of 22

Objective


Describe a sequence of dilations and rigid motions between two figures. Use coordinate points to represent relationships between similar figures.

Common Core Standards


Core Standards

  • 8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
  • 8.G.A.4 — Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Foundational Standards

  • 7.G.A.1
  • 7.RP.A.2

Criteria for Success


  1. Determine if two figures are similar by describing a sequence of dilations and other rigid motions that maps one figure to another. 
  2. Describe sequences of transformations between similar figures; find more than one sequence of transformations.
  3. Determine new coordinates of points that undergo dilations and other transformations.

Tips for Teachers


In this lesson, students combine their understanding of dilations and rigid transformations to determine if two figures are similar in the coordinate plane.

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Anchor Problems

25-30 minutes


Problem 1

Determine using rotations, translations, reflections, and/or dilations whether the two polygons shown below are similar.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Are They Similar?

Are They Similar?, accessed on Oct. 13, 2017, 4:11 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

Triangle $${ABC}$$, shown on the coordinate plane below, is dilated from point $$A$$ by a scale factor of $${\frac{1}{2}}$$ and then translated $$3$$ units down and $$2$$ units left. 

What are the new coordinates for point $${B'}$$?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 3 > Topic A > Lesson 6Teacher Version: Exit Ticket

Grade 8 Mathematics > Module 3 > Topic A > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 3

Rectangle $${{ABCD}}$$ and point $${B'}$$ are shown in the coordinate plane below. Rectangle $${{ABCD}}$$ underwent two transformations, one of which was a dilation.

Describe a possible sequence of transformations that could result in point $$B$$ mapping to point $${B'}$$.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Triangle $$ABC$$ has been dilated by a factor of $$1\over2$$ from the origin to form triangle $$A’B’C’$$. Triangle $$A’’B’’C’’$$ is congruent to triangle $$ABC$$. Describe a sequence of transformations that would map triangle $$A’B’C’$$ to triangle $$A’’B’’C’’$$

Student Response

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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.

Next

Determine and informally prove or disprove if two figures are similar or congruent using transformations.

Lesson 14
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Lesson Map

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

Topic A: Congruence and Rigid Transformations

Topic B: Similarity and Dilations

Topic C: Angle Relationships

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