Name ______Module 2
Similarity Transformations
Learning Target: I can show two figures are similar using a similarity transformation.
Opening Exercise
Given: is the image of after a reflection over .
is the perpendicular bisector of
and are drawn
Using rigid motion, explain why .
Similarity Transformations
In the opening exercise we use rigid motions to show that two figures are congruent. If a series of rigid motions maps one figure onto the other and the figures coincide, we can conclude that they are congruent.
We can use similarity transformations in the same way. Consider Figure 1 below.
From our work on dilations, we can see that there is in fact a dilation that would map figure ?to ?′.
Now examine Figure 2. In Figure 2, the figure ?′ was rotated 90° and is now labeled as ?′′.
It would not be correct to say that ?′′ is a dilation of ? because corresponding segments are neither parallel nor collinear. Yet we saw in Figure 1 that it is possible to transform ?to ?′, which we know to be congruent to ?′′. What are the necessary steps to map ?to ?′′?
If a similarity transformation maps one figure to another, we say the figures are similar. When two figures are similar, corresponding lengths are proportional and corresponding angles are equal in measurement.
1. Figure 1 is similar to Figure 2. Which transformations compose the similarity transformation that maps Figure 1 onto Figure 2?
2. Figure is similar to Figure . Which transformations compose the similarity transformation that
maps onto ?
3. Figure 1 is similar to Figure 2. Which transformations compose the similarity transformation that
maps Figure 1 onto Figure 2?
4. A. Graph and label with vertices A(10, 8), B(6, 4), and C(2, 8).
B. Graph, label, and state the coordinates of , the image of after.
C. Explain why
Name ______Module 2
Similarity TransformationsProblem Set
1. In the diagram below, triangles and are drawn such that and .
Describe a sequence of similarity transformations that shows is similar to .
2. As shown in the diagram below, circle A as a radius of 3 and circle B has a radius of 5. Use
transformations to explain why circles A and B are similar.
3. Given the coordinate plane shown, identify a similarity transformation, mapping onto .
4. Given the diagram below, identify a similarity transformation, if one exists, that maps onto . If one does not exist, explain why. Justify your answer.
5. The diagram below shows a dilation of the plane…or does it? Explain your answer.
6. As shown on the set of axes below, has vertices , , and . Graph and state the coordinates of, the image of after the transformation .
Explain why .
Name ______Module 2
Similarity TransformationsExit Ticket
1. Figure A' is similar to Figure A. Which transformations compose the similarity transformation that maps Figure A onto Figure A'?
2. Given Figure on the coordinate plane shown below, a similarity transformation consists of a dilation centered at the origin with a scale factor of , followed by a reflection over line , then by a vertical translation of units up. Find the image of Figure .