Dilations and Similarity

Lesson 10

Math

Unit 3

10th Grade

Lesson 10 of 18

Objective


Define similarity transformation as the composition of basic rigid motions and dilations. Describe similarity transformation applied to an arbitrary figure.

Common Core Standards


Core Standards

  • G.SRT.A.2 — Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  • G.SRT.B.5 — Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Foundational Standards

  • 8.G.A.4

Criteria for Success


  1. Describe that a similarity transformation is a rigid motion followed by a dilation. 
  2. Prove two figures are congruent by mapping corresponding parts to one another using rigid motions. 
  3. Use similarity to describe two figures that have been transformed by rigid motions and then dilated.
  4. Define congruence as when a figure has undergone a composition of rigid motions and dilation by a scale factor of 1 and the resultant figure is congruent to the starting figure. 
  5. Identify similar figures visually by noticing that they are the same shape but are different “size,” where the sides are proportional and the angle measures are the congruent. 

Tips for Teachers


Ensure that students use the notation for similarity.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes


Problem 1

Below is triangle $$A$$.

Transform triangle $$A$$ according to the rule below, and label the transformed triangle as triangle $$B$$

$${(x,y)\rightarrow(-2(x+2),2(y+2))}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Using the animation shown here, identify the transformations that are done to map the white triangle onto the pink triangle.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

GeoGebra CCSS High School: Geometry (Similarity, Right T, Trig.)3.2 AA Similarity Theorem

CCSS High School: Geometry (Similarity, Right T, Trig.) by Tim Brzezinski is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed Oct. 2, 2017, 10:33 a.m..

Target Task

5-10 minutes


Explain how you know, using transformations, that figure $$A$$ is similar to figure $$B$$.

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.

  • Include problems where students are transforming a figure to produce a similar figure. 
  • Include always, sometimes, never, problems, such as “Two congruent figures are also similar.”
  • Include problems where students need to find the missing measures between two similar figures.

Next

Prove that all circles are similar.

Lesson 11
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Dilations off the Coordinate Plane

Topic B: Dilations on the Coordinate Plane

Topic C: Defining Similarity

Topic D: Similarity Applications

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free