Dilations and Similarity

Lesson 13

Math

Unit 3

10th Grade

Lesson 13 of 18

Objective


Use angle-angle criterion to prove two triangles to be similar.

Common Core Standards


Core Standards

  • G.SRT.A.3 — Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Foundational Standards

  • 7.G.A.2
  • 8.G.A.4

Criteria for Success


  1. Define the angle-angle (AA) criterion for similarity of triangles as “If two angles of two triangles are congruent, then the triangles are similar,” and use this criterion in the development of proofs. 
  2. Define the reflexive property as “If triangle A is similar to triangle B, that means that triangle B is similar to triangle A,” and use this property in the development of proofs. 
  3. Define the transitive property as “If triangle A is similar to triangle B, and triangle B is similar to triangle C, then triangle A is similar to triangle C,” and use this property in the development of proofs.

Tips for Teachers


Criteria for Success #1 is continued from Lesson 12 through Lesson 13.

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Anchor Problems

25-30 minutes


Problem 1

In the diagram below, $${\overline{DE}\parallel{BC}}$$. Prove that $${\triangle ADE \sim \triangle ABC}$$.

Guiding Questions

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Problem 2

In the diagram below, $$D$$ is the midpoint of $${\overline{AB}}$$,  $$F$$ is the midpoint of $${\overline{BC}}$$, and $$E$$ is the midpoint of $${\overline{AC}}$$. Prove that $$\triangle ABC \sim \triangle ADE$$.

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 2 > Topic C > Lesson 15Teacher Version: Problem Set #3

Geometry > Module 2 > Topic C > Lesson 15 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.

Target Task

5-10 minutes


Given the diagram, $${\overline{UX} \perp \overline{VW}}$$ and $${\overline{WY} \perp \overline{UV}}$$. Show that $${\triangle UXV \sim \triangle WYV}$$.

References

EngageNY Mathematics Geometry > Module 2 > Topic C > Lesson 15Teacher Version: Exit Ticket

Geometry > Module 2 > Topic C > Lesson 15 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.

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 need to identify statements that are true about the corresponding parts of similar triangles, dilated triangles, or congruent triangles. 
  • Include error analysis problems where a reason or statement is incorrect or missing from a geometric proof. Correct mistake or fill in reason.

Next

Develop the side splitter theorem and side-angle-side similarity criteria, and use these in the solution of problems.

Lesson 14
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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

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