Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 13
Math
Unit 3
8th Grade
Lesson 13 of 22
Jump To
Lesson Notes
There was an error generating your document. Please refresh the page and try again.
Generating your document. This may take a few seconds.
Are you sure you want to delete this note? This action cannot be undone.
Describe a sequence of dilations and rigid motions between two figures. Use coordinate points to represent relationships between similar figures.
The core standards covered in this lesson
8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
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 combine their understanding of dilations and rigid transformations to determine if two figures are similar in the coordinate plane.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Determine using rotations, translations, reflections, and/or dilations whether the two polygons shown below are similar.
Upgrade to Fishtank Plus to view Sample Response.
Are They Similar?, accessed on Oct. 13, 2017, 4:11 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.
Triangle $${ABC}$$, shown on the coordinate plane below, is dilated from point $$A$$ by a scale factor of $${\frac{1}{2}}$$ and then translated $$3$$ units down and $$2$$ units left.
What are the new coordinates for point $${B'}$$?
Grade 8 Mathematics > Module 3 > Topic A > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Rectangle $${{ABCD}}$$ and point $${B'}$$ are shown in the coordinate plane below. Rectangle $${{ABCD}}$$ underwent two transformations, one of which was a dilation.
Describe a possible sequence of transformations that could result in point $$B$$ mapping to point $${B'}$$.
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
Triangle $$ABC$$ has been dilated by a factor of $$1\over2$$ from the origin to form triangle $$A’B’C’$$. Triangle $$A’’B’’C’’$$ is congruent to triangle $$ABC$$. Describe a sequence of transformations that would map triangle $$A’B’C’$$ to triangle $$A’’B’’C’’$$.
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
Determine and informally prove or disprove if two figures are similar or congruent using transformations.
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.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
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.
8.G.A.38.G.A.4
8.G.A.28.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.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.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
We've got you covered with rigorous, relevant, and adaptable math lesson plans for free