Transformations and Angle Relationships

Lesson 14

Math

Unit 3

8th Grade

Lesson 14 of 22

Objective


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

Common Core Standards


Core Standards

  • 8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
  • 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 and if so, describe the sequence of dilations and rigid transformations that maps one to the other. 
  2. Determine if two figures are congruent, and if so, describe the sequence of rigid transformations that maps one to the other.

Tips for Teachers


  • This lesson continues from Lesson 13 in that all transformations (dilations and rigid motions) are brought together. 
  • This lesson can be used as a flex or review day depending on what students need. 

Lesson Materials

  • Optional: Patty paper (transparency paper) (several sheets per student)
  • Optional: Graph Paper (2-3 sheets per student)
  • Optional: Ruler (1 per student)
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Anchor Problems

25-30 minutes


Problem 1

Figure 1 (F1) and Figure 2 (F2) are shown below. For each statement below, determine if it is true or false. Explain your reasoning.

a.   A reflection over the $$x$$-axis and a translation to the left will transform F1 to F2, making the two figures congruent.

b.   A rotation of $${180^{\circ}}$$ about the origin will transform F1 to F2, making the two figures congruent.

c.   A dilation from the origin and a translation up will transform F1 to F2, making the two figures similar.

d.   A reflection across the $$x$$-axis and a reflection across the $$y$$-axis will transform F1 to F2, making the two figures congruent.

e.   There is no sequence that will transform Figure 1 to Figure 2, making the two figures neither congruent nor similar.

Guiding Questions

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Student Response

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Problem 2

The pentagon shown below is the resulting image of pentagon $${ABCDE}$$ after it was dilated from point $$A$$ by a scale factor of $${\frac{1}{2}}$$ and then rotated clockwise $${90^{\circ}}$$ about point $$A$$

What are the original coordinates of pentagon $${ABCDE}$$?

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


Determine if the two figures shown below are congruent, similar, or neither. Prove your answer using transformations.

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.

  • Multiple-choice options are good problems to engage students in evaluating multiple possible answer choices. Examples to include:
    • Given similar or congruent figures, select the correct description of the transformation sequence.
    • Multiple-select items about properties of transformations where there is more than one correct answer.

Next

Find missing side lengths in similar figures. Find scale factor between similar figures.

Lesson 15
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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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