Curriculum  /  Math  /  10th Grade  /  Unit 3: Dilations and Similarity  /  Lesson 5

Dilations and Similarity

Lesson 5

Math

Unit 3

10th Grade

Lesson 5 of 18

Objective

Dilate a figure from a point on the figure. Use the properties of dilations with respect to parallel lines to verify dilations and find the center of dilation.

Common Core Standards

Core Standards

  • G.CO.D.12 — Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
  • G.SRT.A.1.A — A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
  • 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

  • 8.G.A.1

Criteria for Success

  1. Describe that a line segment through the center of dilation will map to another line segment on that line when dilated. 
  2. Describe that a line segment not through the center of dilation will map to a line segment parallel to the original line segment. 
  3. Use constructions to dilate a figure. 
  4. Explain the properties of parallel lines as they relate to dilations. 
  5. Identify the center of dilation from a figure and its dilated image using constructions. 
  6. Describe how you know that the figure formed through constructions is a dilation of the original, even when the original is embedded in the new figure. 
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Anchor Problems

25-30 minutes

Problem 1

Draw a sketch of $${\triangle ABC}$$ scaled by a factor of $$2$$ from the center identified below:

From a Center of B From a Center of C From a Center of A

 

Guiding Questions

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Problem 2

Construct the dilation of $${\triangle ABC}$$, with point $$B$$ as the center of dilation and a scale factor of $${2.}$$ 

Guiding Questions

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Problem 3

How do you know that rectangle $${A'BC'D'}$$ is a dilation of rectangle $${ABCD}$$?

 

 

Guiding Questions

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Target Task

5-10 minutes

Dilate the following figure by a scale factor of $$2$$ with a center of dilation of point $$E$$.

Dilate the same figure by a scale factor of $$2$$ with a center of dilation of point $$B$$. 

 

  • Describe the parallel, proportional, and congruent relationships that exist within each of these dilations. 
  • How are these dilations different? The same?

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 “always, sometimes, never” problems such as “Identify whether the following statement is always, sometimes, or never true: A line segment that is dilated will map to a parallel line segment.”

Next

Prove that a line parallel to one side of a triangle divides the other two sides proportionally.

Lesson 6
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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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