Dilations and Similarity

Lesson 18

Math

Unit 3

10th Grade

Lesson 18 of 18

Objective


Solve real-life problems with two different centers of dilation.

Common Core Standards


Core Standards

  • G.SRT.B.4 — Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
  • 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 parallel lines cut transversals into proportional segments
  2. Dilate a figure about two different centers of dilation but with the same scale factor. 
  3. Describe why the dilated figures are congruent to one another.

Tips for Teachers


  • This is a performance task lesson. This is based on the MARS Formative Assessment Lesson for High School, “Deducting Relationships: Floodlight Shadows.”
  • Students may need some background knowledge on floodlights. Refer to the MARS lesson as well as the following resource for students to see how three spotlights work together in tandem: Laughing Squid, “Shadow, A Solo Dance Performance Illuminated by Three Synchronized Spotlight Drones,” by E.D.W. Lynch.
  • There is no specific Problem Set Guidance or Target Task for this lesson because it is a performance task. Ensure that review problems are available for students who finish early or who need some additional practice in the skills of the unit to support this task.
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Anchor Problems


Eliot is playing football at night when two spotlights come on. 

  • Eliot is 6 ft. tall. 
  • He stands exactly halfway between two spotlights
  • The spotlights are 12 yards high, and 50 yards apart. 
  • The spotlights give Eliot two shadows, falling in opposite directions. 

Part A: Draw a diagram to represent this situation.  Be sure to label all quantities. 

Part B: What is the total length of Eliot’s shadows. Explain your reasoning below. 

Part C: Suppose Eliot walks in a straight line toward one of the floodlights.  How does this movement change the total length of Eliot’s shadows?

Guiding Questions

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References

MARS Formative Assessment Lessons for High School Deducting Relationships: Floodlight Shadows

Deducting Relationships: Floodlight Shadows from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Oct. 20, 2017, 10:16 a.m..

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Lesson 17

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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