Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 14
Math
Unit 3
8th Grade
Lesson 14 of 22
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Determine and informally prove or disprove if two figures are similar or congruent using transformations.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
7.G.A.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
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
25-30 minutes
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.
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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 $${ABCDE}$$?
A set of suggested resources or problem types that teachers can turn into a 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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Determine if the two figures shown below are congruent, similar, or neither. Prove your answer using transformations.
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.
Next
Find missing side lengths in similar figures. Find scale factor between similar figures.
Topic A: Congruence and Rigid Transformations
Understand the rigid transformations that move figures in the plane (translation, reflection, rotation).
Standards
8.G.A.1.A8.G.A.1.B8.G.A.1.C8.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.A8.G.A.1.B8.G.A.1.C8.G.A.28.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.28.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.38.G.A.4
8.G.A.28.G.A.4
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.28.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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