Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 2
Math
Unit 3
8th Grade
Lesson 2 of 22
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Describe and perform translations between congruent figures. Use translations to determine if figures are congruent.
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 essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Lessons 2 and 3 are on translations. Lesson 2 focuses on students understanding how to perform translations and how to talk about them. Students should now be starting to use the mathematical language "translation", compared to more informal vocabulary used in Lesson 1.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
You want to prove that $${{ABCD}}$$ and $${{A'B'C'D'}}$$ are congruent by using a translation. Explain how you could translate $${{ABCD}}$$ onto $${{A'B'C'D'}}$$ so that they overlap perfectly. Be specific and use the coordinate plane as a reference.
Figure $${ABC}$$ is shown in the coordinate plane.
a. Translate figure $${ABC}$$ 3 units to the right and 2 units up. Name and label the new figure.
b. How are the two figures the same?
c. How are the two figures different?
Figure 1 is congruent to Figure 2.
Which statement demonstrates the congruency between the two figures?
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Two figures are shown in the coordinate plane. Alex thinks that the two figures are congruent because figure $${QRS}$$ could be translated 5 units to the left and 2 units down to map to figure $${Q'R'S'}$$.
a. Explain why Alex’s thinking is incorrect.
b. How would you change figure $${Q'R'S'}$$ so it is congruent to figure $${QRS}$$? What translation would prove the congruence between the two figures?
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.
Lesson 1
Lesson 3
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 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 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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