Dilations and Similarity

Lesson 16

Math

Unit 3

10th Grade

Lesson 16 of 18

Objective


Use the side-side-side criteria for similarity and other similarity and congruence theorems in the solution of problems.

Common Core Standards


Core Standards

  • 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. Identify the definitions and examples that support a claim. 
  2. Analyze the conditions under which a claim might be true. 
  3. Use theorems/postulates/etc., strategically to establish coherent and efficient reasoning. Use theorems that involve lines and angles related to: 
    1. Parallel line diagrams
    2. Parallelograms
    3. Triangles
    4. Congruent figures
    5. Similar figures
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Anchor Problems


Problem 1

Are the two triangles shown below similar? Why or why not?

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 2 > Topic C > Lesson 17Exercise 3

Geometry > Module 2 > Topic C > Lesson 17 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

Determine if each statement is always, sometimes, or never true. Explain your reasoning. 

  • Alternate exterior angles of two lines, intersected by a third, will be parallel. 
  • A dilation of a line segment will result in a parallel line segment. 
  • A dilation of an angle will result in a congruent angle. 
  • A dilation of an angle will increase or decrease the measure of the angle by the scale factor. 
  • A line segment drawn parallel to one side of a triangle will split the other two sides of the triangle into congruent parts. 
  • The angle bisector of any angle in a triangle divides a triangle into similar triangles. 
  • A dilation of k=1 will result in a congruent figure. 

Guiding Questions

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Target Task


Determine if the statement below is always, sometimes, or never true. Explain your reasoning. 

“To prove two triangles similar, you need to prove that two of the corresponding sides are proportional.”

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 that require the use of at least two congruence or similarity theorems to complete a proof. 
  • Include problems where there is a missing statement or reason in a proof and the student needs to identify what is missing. 
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Lesson 15

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Lesson 17

Lesson Map

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Topic A: Dilations off the Coordinate Plane

Topic B: Dilations on the Coordinate Plane

Topic C: Defining Similarity

Topic D: Similarity Applications

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