Lesson 15 | Transformations and Angle Relationships | 8th Grade Mathematics

Objective

Find missing side lengths in similar figures. Find scale factor between similar figures.

Common Core Standards

Core Standards

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.

Geometry

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.

Foundational Standards

The foundational standards covered in this lesson

7.G.A.1

Geometry

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

Ratios and Proportional Relationships

7.RP.A.2 — Recognize and represent proportional relationships between quantities.
7.RP.A.3

Ratios and Proportional Relationships

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Use ratio reasoning between corresponding sides in similar figures to determine missing measurements.
Find the scale factor between similar figures and use it to find missing measurements.
Determine if two figures are similar by testing for a scale factor between the side lengths.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

In this lesson, students apply the concept of scale factor to determine if shapes are similar with proportional corresponding sides.

Fishtank Plus

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Two triangles are shown below. The measure of angle $$A$$ is equal to the measure of angle $$D$$. (Figures are not drawn to scale.)

a. Explain, using transformations, how you know the two triangles are similar.

b. Find the value for the side length marked $$x$$.

Guiding Questions

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Problem 2

Are triangles $${{ABC}}$$ and $${{EFG}}$$ similar? Explain your answer.

Sketch a triangle that is similar to either triangle $${{ABC}}$$ or triangle $${{EFG}}$$. Label the side lengths.

Guiding Questions

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Problem 3

Triangle $${{ABC}}$$ is similar to triangle $${{ADE}}$$. The measure of $${\overline{AB}}$$ is approximately $${3.16}$$ units.

a. Find the scale factor from triangle $${{ABC}}$$ to $${{ADE}}$$.

b. Find the approximate measure of $${\overline{AD}}$$.

Guiding Questions

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Problem Set

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Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Three parallelograms are shown below. Which parallelogram, either $$B$$ or $$C$$, is similar to parallelogram $$A$$? Justify your response.

Problem 2

Triangles $$QRS$$ and $$JKL$$ are similar. Use the diagrams below to answer the following questions.

a. What is the length of line segment $$SR$$? Show or explain your reasoning.

b. What is the length of line segment $$JK$$? Show or explain your reasoning.

Student Response

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Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

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.

Open Up Resources Grade 8 Unit 2 Practice Problems — Lesson 7 #1-4
EngageNY Mathematics Grade 8 Mathematics > Module 3 > Topic B > Lesson 11 — Teacher Version: Do not include items that involve the Fundamental Theorem of Similarity or Angle-Angle criterion, as those concepts have not been covered.

Lesson 14

Lesson 16

Lesson Map

Topic A: Congruence and Rigid Transformations

Understand the rigid transformations that move figures in the plane (translation, reflection, rotation).