Dilations and Similarity

Lesson 17

Math

Unit 3

10th Grade

Lesson 17 of 18

Objective


Solve for measurements involving right triangles using scale factors and ratios.

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 similar figures in contextual situations involving shadows and light.
  2. Use similarity relationships to find missing side lengths (called “indirect measurement”) using relationships between and within similar figures. 
  3. Find missing measurements directly and algebraically. 
  4. Describe that the relationship within sides of similar triangles is equivalent, and distinguish this relationship from the scale factor between similar triangles. 
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Anchor Problems


Problem 1

What do you notice?

Guiding Questions

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Problem 2

What is the height of the tree?

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 2 > Topic C > Lesson 16Teacher Version: Opening Exercise

Geometry > Module 2 > Topic C > Lesson 16 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 3

Draw a diagram that represents the following information.


Given the following information: 
$${\overline{AB} \parallel \overline{DE}}$$

$${A,D,C}$$ are collinear
$${B,E,C}$$ are collinear
$${DE=12m}$$
$${EC=8m}$$
$${AB=18m}$$
$${CB=12m}$$


Identify three ratios between side lengths that are proportional.

Guiding Questions

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Target Task


Dennis needs to fix a leaky roof on his house but does not own a ladder. He thinks that a 25 ft. ladder will be long enough to reach the roof, but he needs to be sure before he spends the money to buy one. He chooses a point $$P$$ on the ground where he can visually align the roof of his car with the edge of the house roof. Help Dennis determine if a 25 ft. ladder will be long enough for him to safely reach his roof.

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References

EngageNY Mathematics Geometry > Module 2 > Topic C > Lesson 16Teacher Version: Exit Ticket

Geometry > Module 2 > Topic C > Lesson 16 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..

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.

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Lesson 16

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Lesson 18

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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