Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 5
Math
Unit 3
8th Grade
Lesson 5 of 22
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Describe sequences of transformations between figures using reflections and translations. Use coordinate points to represent relationships between reflected figures.
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.
8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Figure 1 is reflected over the $$y$$-axis to create Figure 2, as shown in the coordinate plane below.
a. Describe what you notice about the coordinate points of a figure when it is reflected over the $$y$$-axis.
b. What do you think happens to coordinate points of a figure when it is reflected over the $$x$$-axis?
Triangles $${{ABC}}$$ and $${{PQR}}$$ are shown below in the coordinate plane.
Describe a sequence of transformations that can map $${{ABC}}$$ to $${{PQR}}$$.
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Below is a picture of a triangle on a coordinate grid:
a. Draw the reflection of $${\triangle ABC}$$ over the vertical line through $${x=-2}$$. Label the image of $$A$$ as $$A'$$, the image of $$B$$ as $$B'$$, and the image of $$C$$ as $$C'$$.
b. Draw the reflection of $${\triangle A'B'C'}$$ over the vertical line through $$x=2$$. Label the image of $$A'$$ as $$A''$$, the image of $$B'$$ as $$B''$$, and the image of $$C'$$ as $$C''$$.
c. What single rigid transformation of the plane will map $${\triangle ABC}$$ to $${\triangle A''B''C''}$$? Explain.
Reflecting Reflections, accessed on Oct. 13, 2017, 4 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 4
Lesson 6
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 and perform rotations between congruent figures.
Describe sequences of transformations between figures using rotations and other transformations.
Describe a sequence of rigid transformations that will map one figure onto another.
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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