Transformations and Angle Relationships
Lesson 15
Objective
Find missing side lengths in similar figures. Find scale factor between similar figures.
Common Core Standards
Core Standards
?
-
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
?
-
7.G.A.1
-
7.RP.A.2
-
7.RP.A.3
Criteria for Success
?
- 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
?
In this lesson, students apply the concept of scale factor to determine if shapes are similar with proportional corresponding sides.
Remote Learning Guidance
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example) and Anchor Problem 2 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.
Anchor Problems
?
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.)
- Explain, using transformations, how you know the two triangles are similar.
- Find the value for the side length marked $$x$$.
Guiding Questions
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
Problem 3
Triangle $${{ABC}}$$ is similar to triangle $${{ADE}}$$. The measure of $${\overline{AB}}$$ is approximately $${3.16}$$.
- Find the scale factor from triangle $${{ABC}}$$ to $${{ADE}}$$.
- Find the approximate measure of $${\overline{AD}}$$.
Guiding Questions
Problem Set
?
The following resources include problems and activities aligned to the objective of the lesson that can be used 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.
Target Task
?
Problem 1
In the diagram below, you have triangle $${ABC}$$ and triangle $${A'B'C'}$$. Based on the information given, are the two triangles similar? Explain your answer.
References
Grade 8 Mathematics > Module 3 > Topic B > Lesson 11 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..
Modified by Fishtank Learning, Inc.Problem 2
In the diagram below, triangle $${ABC}$$ is similar to triangle $${DEF}$$. Use the information to answer the two parts below.
- Determine the length of side $${\overline{AB}}$$.
- Determine the length of side $${\overline{DF}}$$.
References
Grade 8 Mathematics > Module 3 > Topic B > Lesson 11 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..
Modified by Fishtank Learning, Inc.Mastery Response
?