Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 11
Math
Unit 3
8th Grade
Lesson 11 of 22
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Define a dilation as a non-rigid transformation, and understand the impact of scale factor.
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.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Several figures are shown below.
a. What do you notice? What do you wonder about the relationships between the shapes?
b. A dilation is a transformation that enlarges or shrinks a figure in a proportional way so that the shape remains the same. Where do you see evidence of a dilation in the figures?
Triangle $${ABC}$$ is dilated to create similar triangle $${DEF}$$.
a. Indicate the corresponding angles in the diagram. What is the relationship between corresponding angles?
b. Name the corresponding sides in the diagram. What is the relationship between corresponding side lengths?
Sketch an image of each figure after the dilations described below. The figures do not need to be drawn exactly to size but should include the lengths of the sides.
a. Triangle $${LMN}$$ is dilated by a scale factor of 3.
b. Rectangle $${ABCD}$$ is dilated by a scale factor of $${\frac{1}{2}}$$.
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Trapezoid $${ABCD}$$, shown below, is dilated by a scale factor of $${\frac{1}{4}}$$. Angle $$D$$ is a right angle.
a. Which statements are true? Select all that apply.
a. $${\overline{C'D'}}$$ will be $${48}$$ units long.
b. $${\overline{B'C'}}$$ will be $${2\frac{1}{2}}$$ units long.
c. $${{\overline{A'D'}}}$$ will be $${15}$$ units long.
d. The measure of $${{\angle B}'}$$ will be $${\frac{1}{4}}$$ the measurement of $${\angle B}$$.
e. $${\angle D'}$$ will be a right angle.
f. $${\overline {B'C'}}$$ will be parallel to $${{\overline{A'D'}}}$$.
g. Figure $${A'B'C'D'}$$ will be a trapezoid.
b. Explain your response to answer choices (b) and (d). Why did you decide that those answer choices were true or false?
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Lesson 10
Lesson 12
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
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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