Dilations and Similarity

Lesson 1

Math

Unit 3

10th Grade

Lesson 1 of 18

Objective


Describe properties of scale drawings.

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.

Foundational Standards

  • 7.G.A.1
  • 8.G.A.4

Criteria for Success


  1. Describe how a figure can be stretched either horizontally, vertically, or in all directions by the same factor. 
  2. Define a proportional stretch or shrink as scaling a figure by the same factor in all directions. 
  3. Define the scale factor as the multiplicative value you stretch or shrink a figure proportionally. 
  4. Describe that when a figure is proportionally stretched or shrunk, the corresponding side lengths between the image and the pre-image are proportional. 
  5. Describe that when a figure is proportionally stretched or shrunk, the corresponding angles remain congruent. 
  6. Develop the understanding that a scale factor between zero and one shrinks a figure, a scale factor greater than one stretches a figure, and a scale factor that is equal to one produces a congruent figure.
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Anchor Problems

25-30 minutes


Problem 1

Below is an image of a bicycle.



Which of the images below appears to be scaled proportionally to the bicycle shown above and why?

Guiding Questions

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Problem 2

The two triangles below are scaled figures of one another. Describe how you know this to be true.

Guiding Questions

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Target Task

5-10 minutes


The figures above are scaled well. Which of the following statements must be true? Select all that apply. 

  1. The corresponding angle measures are congruent. 
  2. The corresponding angle measures are shrunk proportionally. 
  3. The corresponding side lengths are congruent. 
  4. The corresponding side lengths are shrunk proportionally. 
  5. The figure has only been shrunk horizontally. 
  6. The figure has a negative scale factor. 
  7. The figure has a scale factor that is a positive fraction

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 such as: 
    • If ___ measures ___ degrees, how many degrees do you think the corresponding angle on the scaled figure will be? 
    • If you scale a figure and then scale it back to the original, what will the relationship between the scale factors be? 
    • A figure is scaled by 0.5 and then that figure is scaled by 0.5. What is the scale factor between the original figure and the final figure? 
    • Write a statement that describes the value of a scale factor that will stretch a figure and the value of a scale factor that will shrink a figure. 
  • Include “always, sometimes, never” style problems. For example, “State whether the following is always, sometimes, or never true. Explain your reasoning. The corresponding angles of both a pre-image and image are congruent when stretched by a factor of two horizontally.”

Next

Define and describe the characteristics of dilations. Dilate figures using constructions when the center of dilation is not on the figure.

Lesson 2
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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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