Geometry Lesson 7.6.notebook
March 18, 2015
Similarity Transformations
A similarity transformation is a transformation produces a figure that is similar to the preimage (the original figure). These changes in sizes are called dilations.
A dilation will either enlarge or reduce the original figure proportionally.
This new figure is called a similarity transformation.
Dilations are performed with respect to a fixed point called the center of dilation.
The scale factor of the dilation describes the extent of the dilation. The scale factor is the ratio of a length on the new image to a corresponding length on the preimage (original figure).
There are two types of dilations, enlargements and reductions.
Enlargement ­ A dilation with a scale factor > 1.
Reduction ­ A dilation with a scale factor between 0 and 1. 0 < sf < 1.
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Geometry Lesson 7.6.notebook
March 18, 2015
Refer to the figure on the coordinate plane. Determine whether the dilation from A to B is an enlargement or a reduction. Then fine the scale factor of the dilation.
a. Triangle A has coordinates of (­3,2), (3,2) and (1, ­3)
Triangle B has coordinates of (­1.5, 1), (1.5,1) and (0.5, ­1.5)
Since A is larger than B, that is to get from A to B the figure gets
smaller. So, this is a reduction.
To find the scale factor find the distance between corresponding vertices for triangle A
and corresponding vertices for triangle B.
Triangle A = Triangle B = scale factor = So the scale factor of this reduction is .
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Geometry Lesson 7.6.notebook
March 18, 2015
Try example 1B on P. 506.
1. Adrianna uses a copier to enlarge a movie ticket to use as a background for a page in her movie ticket scrapbook. By what percent should she enlarge the ticket stub so that the dimensions of the image are 3 times that of her original? What will the dimensions of the enlarged image be?
a. The scale factor of her enlargement is 3. Multiply the scale factor
by 100% to get the percent of enlargement.
TICKET
b. Take the dimensions of the ticket and multiply each on by 300%
to get the new dimensions. 2. If the resulting ticket stub image was 1.5 cm wide by 1.9 cm long instead, what percent did Adrianna mistakenly dilate the original image?
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Geometry Lesson 7.6.notebook
March 18, 2015
Verify a Similarity after a Dilation
3. Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation.
a. original: J(­6, 4), K(6,8), L(8,2), M(­4, ­2)
image: P(­3,2), Q(3,4), R(4,1), S(­2, ­1)
Use distance formula to find length of all the sides. Then set up proportions to verify similarity transformation.
Since the sides have a scale factor of 1/2, this verifies that we have a similarity transformation by SSS.
Remember, with these types of transformations, we will uses SSS or SAS.
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Geometry Lesson 7.6.notebook
March 18, 2015
P. 508 6­14, 16
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