Transformations and Angle Relationships
Lesson 14
Objective
Determine and informally prove or disprove if two figures are similar or congruent using transformations.
Common Core Standards
Core Standards
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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.
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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
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7.G.A.1
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7.RP.A.2
Criteria for Success
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- Determine if two figures are similar and if so, describe the sequence of dilations and transformations that maps one to the other.
- Determine if two figures are congruent, and if so, describe the sequence of rigid transformations that maps one to the other.
Tips for Teachers
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- 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.
- The following materials are useful for this lesson: patty paper (or transparency paper), graph paper, and rulers.
Remote Learning Guidance
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from discussion) . Find more guidance on adapting our math curriculum for remote learning here.
Anchor Problems
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Problem 1
Two figures are shown below.
For each statement below, determine if it is true or false. Explain your reasoning.
- A reflection over the $$x$$-axis followed by a translation to the left will transform Figure 1 to Figure 2, making the two figures congruent.
- A rotation of $${180^{\circ}}$$ about the origin will transform Figure 1 to Figure 2, making the two figures congruent.
- A dilation from the origin and a translation up will transform Figure 1 to Figure 2, making the two figures similar.
- A reflection across the $$y$$-axis followed by a reflection across the $$y$$-axis will transform Figure 1 to Figure 2, making the two figures congruent.
- There is no sequence that will transform Figure 1 to Figure 2, making the two figures neither congruent nor similar.
Guiding Questions
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
Problem Set
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The following resources include problems and activities aligned to the objective of the lesson that can be used 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.
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PARCC Released Items Math Spring Operational 2016 Grade 8 Released Items
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Problem #18
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EngageNY Mathematics Grade 8 Mathematics > Module 3 > Topic B > Lesson 8
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Teacher Version: Problem Set #1-6
Target Task
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Determine if the two figures shown below are congruent, similar, or neither. Prove your answer using transformations.
Mastery Response
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