Grade 8 Module 3 Similarity - · PDF fileDEPARTMENT OF DEFENSE EDUCATION ACTIVITY...

D E PA R T M E N T O F D E F E N S E E D U C AT I O N A C T I V I T Y
Incorporating DoDEAs College and Career Ready Standards for Mathematics
Grade 8 Module 3Similarity
Student Materials
From EngageNY.org of the New York State Education Department. Grade 8 Module 3: Similarity. Internet. Available from: https://www.engageny.org/resource/grade-8-mathematics-module-3 accessed 4/28/16.
*The original work has been modified by removing the "New York State Common Core" page header and associated symbols, and adding a DoDEA cover page.

DoDEA College and Career Ready 83 Lesson 1
Lesson 1: What Lies Behind Same Shape? S.1
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Lesson 1: What Lies Behind Same Shape?
Classwork
Exploratory Challenge
Two geometric figures are said to be similar if they have the same shape but not necessarily the same size. Using that informal definition, are the following pairs of figures similar to one another? Explain.
Pair A:
Pair B:
Pair C:
Pair D:
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Pair E:
Pair F:
Pair G:
Pair H:
Exercises
1. Given || = 5 in.a. If segment is dilated by a scale factor = 4, what is the length of segment ?
b. If segment is dilated by a scale factor = 12 , what is the length of segment ?

Use the diagram below to answer Exercises 26. Let there be a dilation from center . Then, () = and () = . In the diagram below, || = 3 cm and || = 4 cm, as shown.
2. If the scale factor is = 3, what is the length of segment ?
3. Use the definition of dilation to show that your answer to Exercise 2 is correct.
4. If the scale factor is = 3, what is the length of segment ?
5. Use the definition of dilation to show that your answer to Exercise 4 is correct.
6. If you know that || = 3, || = 9, how could you use that information to determine the scale factor?

Problem Set
1. Let there be a dilation from center . Then, () = and () = . Examine the drawing below.What can you determine about the scale factor of the dilation?
Lesson Summary
Definition: For a positive number , a dilation with center and scale factor is the transformation of the plane that maps to itself, and maps each remaining point of the plane to its image on the ray so that || =||. That is, it is the transformation that assigns to each point of the plane a point () so that
1. () = (i.e., a dilation does not move the center of dilation).
2. If , then the point () (to be denoted more simply by ) is the point on the ray so that|| = ||.
In other words, a dilation is a rule that moves each point along the ray emanating from the center to a new point on that ray such that the distance || is times the distance ||.

2. Let there be a dilation from center . Then, () = , and () = . Examine the drawingbelow. What can you determine about the scale factor of the dilation?
3. Let there be a dilation from center with a scale factor = 4. Then, () = and () = .|| = 3.2 cm, and || = 2.7 cm, as shown. Use the drawing below to answer parts (a) and (b). The drawing isnot to scale.
a. Use the definition of dilation to determine ||.b. Use the definition of dilation to determine ||.

4. Let there be a dilation from center with a scale factor . Then, () = , () = , and() = . || = 3, || = 15, || = 6, and || = 5, as shown. Use the drawing below to answerparts (a)(c).
a. Using the definition of dilation with lengths and , determine the scale factor of the dilation.b. Use the definition of dilation to determine ||.c. Use the definition of dilation to determine ||.

Lesson 2: Properties of Dilations S.7
Lesson 2: Properties of Dilations
Classwork
Examples 12: Dilations Map Lines to Lines

Example 3: Dilations Map Lines to Lines
Exercise
Given center and triangle , dilate the triangle from center with a scale factor = 3.
a. Note that the triangle is made up of segments , , and . Were the dilated images of thesesegments still segments?

b. Measure the length of the segments and . What do you notice? (Think about the definition ofdilation.)
c. Verify the claim you made in part (b) by measuring and comparing the lengths of segments and andsegments and . What does this mean in terms of the segments formed between dilated points?
d. Measure and . What do you notice?
e. Verify the claim you made in part (d) by measuring and comparing the following sets of angles: (1) and and (2) and . What does that mean in terms of dilations with respect to angles andtheir degrees?

Problem Set
1. Use a ruler to dilate the following figure from center , with scale factor = 12.
Lesson Summary
Dilations map lines to lines, rays to rays, and segments to segments. Dilations map angles to angles of the same degree.
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Grade 8 Module 3 Similarity - · PDF fileDEPARTMENT OF DEFENSE EDUCATION ACTIVITY...

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