Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 12
Math
Unit 3
8th Grade
Lesson 12 of 22
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Describe and perform dilations.
The core standards covered in this lesson
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
Suggestions for teachers to help them teach this lesson
In this lesson, students work with dilations in isolation, distinguishing between points of origin on and off of the figure. In the next lessons, students will work with both dilations and rigid transformations.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Two diagrams below show a dilation of Rectangle $${ABCD}$$ by a scale factor of 2.
If the scale factor is the same, then why do the two diagrams show different dilated figures?
Rectangle $${ABCD}$$ is similar to rectangle $${{A'B'C'D'}}$$ because it can be dilated to map onto $${{A'B'C'D'}}$$.
Describe the transformation. Include the scale factor and center point of dilation.
Angle $${EFG}$$ is shown in the coordinate plane below.
Dilate the angle by a scale factor of 2 with the center of dilation at the origin.
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
Consider triangle $${ABC}$$.
a. Draw a dilation of $${ABC}$$ with center $$A$$ and scale factor 2.
b. Draw a dilation of $${ABC}$$ with center $$B$$ and scale factor 3.
c. Draw a dilation of $${ABC}$$ with center $$C$$ and scale factor $${\frac{1}{2}}$$.
Effects of Dilations on Length, Area, and Angles, accessed on June 4, 2018, 1:48 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.
Use the dilations from Target Task Problem 1 to answer the questions.
a. For each dilation, by what factor do the base and height of the triangle change?
b. For each dilation, by what factor does the area of the triangle change? Explain.
c. For each dilation, how do the angles of the scaled triangle compare to the original?.
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 11
Lesson 13
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 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 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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