Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 8
Math
Unit 3
8th Grade
Lesson 8 of 22
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Describe a sequence of rigid transformations that will map one figure onto another.
The core standards covered in this lesson
8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.
8.G.A.1.B — Angles are taken to angles of the same measure.
8.G.A.1.C — Parallel lines are taken to parallel lines.
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.
The foundational standards covered in this lesson
4.MD.C.6 — Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Triangle $${{ABC}}$$ has been moved according to the following sequence: a translation followed by a rotation followed by a reflection.
With precision, describe each rigid motion that would map triangle $${{ABC}}$$ onto triangle $${LMN}$$.
Grade 8 Mathematics > Module 2 > Topic B > Lesson 10 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..
Avik believes that Figure 1 and Figure 2, shown below, are congruent because he can use two reflections to map one figure to the other.
Sonya also believes the two figures are congruent because she can use a single rotation to map one figure to the other.
Are both Avik and Sonya right? Explain with precision the transformation(s) that will show the two figures are congruent.
Rectangle $${{ABCD}}$$ and $${{A'B'C'D'}}$$ are shown below.
Which sequence of transformations show that rectangle $${{ABCD}}$$ and rectangle $${{A'B'C'D'}}$$ are congruent? Select all that apply.
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The two triangles in the picture below are congruent:
a. Give a sequence of rotations, translations, and/or reflections that take $${\triangle PRQ}$$ to $${\triangle ABC}$$.
b. Is it possible to show the congruence in part (a) using only translations and rotations? Explain.
Congruent Triangles, accessed on Oct. 13, 2017, 4:04 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.
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Lesson 7
Lesson 9
Topic A: Congruence and Rigid Transformations
Understand the rigid transformations that move figures in the plane (translation, reflection, rotation).
8.G.A.1.A 8.G.A.1.B 8.G.A.1.C 8.G.A.2
Describe and perform translations between congruent figures. Use translations to determine if figures are congruent.
Describe and apply properties of translations. Use coordinate points to represent relationships between translated figures.
8.G.A.1.A 8.G.A.1.B 8.G.A.1.C 8.G.A.2 8.G.A.3
Describe and perform reflections between congruent figures. Use reflections to determine if figures are congruent.
Describe sequences of transformations between figures using reflections and translations. Use coordinate points to represent relationships between reflected figures.
Describe and perform rotations between congruent figures.
Describe sequences of transformations between figures using rotations and other transformations.
Describe multiple rigid transformations using coordinate points.
8.G.A.2 8.G.A.3
Review rigid transformations and congruence between two figures.
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Topic B: Similarity and Dilations
Define a dilation as a non-rigid transformation, and understand the impact of scale factor.
8.G.A.4
Describe and perform dilations.
Describe a sequence of dilations and rigid motions between two figures. Use coordinate points to represent relationships between similar figures.
8.G.A.3 8.G.A.4
Determine and informally prove or disprove if two figures are similar or congruent using transformations.
8.G.A.2 8.G.A.4
Find missing side lengths in similar figures. Find scale factor between similar figures.
Use properties of similar triangles to model and solve real-world problems.
Topic C: Angle Relationships
Define and identify corresponding angles in parallel line diagrams. Review vertical, supplementary, and complementary angle relationships.
8.G.A.2 8.G.A.5
Define and identify alternate interior and alternate exterior angles in parallel line diagrams. Find missing angles in parallel line diagrams.
Solve for missing angle measures in parallel line diagrams using equations.
8.G.A.5
Define and use the interior angle sum theorem for triangles.
Define and use the exterior angle theorem for triangles.
Define and use the angle-angle criterion for similar triangles.
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