4.6 Similarity and Transformations

​4.6 Similarity Transformations

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"Mathematics is the music of reason"

-James Joseph Sylvester

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Multiple Choice

Which choice correctly describes similar figures?

• Same shape and same size

• Same shape but not necessarily the same size.

• Same size but not necessarily the same shape.

• None of the above

Multiple Choice

Find the image of the $$\Delta$$  with vertices  $$P\left(-1,5\right),\ Q\left(-4,3\right),\ R\left(-2,1\right)$$  after the similarity transformation: 

Rotation 180 degrees about the origin AND Dilation:  $$\left(x,y\right)\rightarrow\left(2x,2y\right)$$   (NOT ON THE PACKET)

• $$P''\left(-10,1\right),\ Q''\left(-6,\ 8\right),\ R''\left(-2,\ 4\right)$$  

• $$P''\left(5,-1\right),\ Q''\left(3,-4\right),\ R''\left(1,-2\right)$$  

• $$P''\left(1,-5\right),\ Q''\left(4,-3\right),\ R''\left(2,-1\right)$$  

• $$P''\left(2,-10\right),\ Q''\left(8,-6\right),\ R''\left(4,-2\right)$$  

Multiple Choice

Which similarity transformation maps ABCD to A'B'C'D'? #11

• A $$180\degree$$ rotation followed by a dilation with scale factor 3

• A reflection in the x-axis followed by a dilation with scale factor 3.

• A $$\frac{1}{3}$$ rotation followed by a dilation with scale factor

• A reflection in the x-axis followed by a dilation with scale factor $$\frac{1}{3}$$

Multiple Choice

Which similarity transformation maps WXYZ to W'X'Y'Z'? #12

• Reflection over the x-axis, followed by a dilation with a scale factor of 2 

•  Reflection over the y-axis, followed by a dilation with a scale factor of 2 

• Reflection over the y-axis, followed by a dilation with a scale factor of  $$\frac{1}{2}$$

• Reflection over the x-axis, followed by a dilation with a scale factor of  $$\frac{1}{2}$$   

Multiple Choice

Quadrilateral OBCD is similar to Quadrilateral OHTE because? #8

• Quad OBCD can be reflected over the x axis and then rotated 90 degrees

• Quad OBCD can be reflected over the x-axis and then dilated about point O by a scale factor of 2.

• Quad OBCD can be reflected over the y-axis and then dilated about the origin by a scale factor of 2.

• Quad OBCD can be reflected over the y-axis and then dilated about the origin by a scale factor of 1/2.

Multiple Choice

ΔOBC is similar to ΔOGT because: (choose the best answer) #9

• ΔOBC can be dilated about point O by a scale factor of 1/2, and then rotated 90 degrees about the origin

• ΔOBC can be dilated about point G by a scale factor of 1/2, and then reflected over the x- axis

• They aren't similar

• They map to each other with similarity transformations.

Multiple Select

Select ALL sequences of transformations that would show that

$$\Delta ABC$$   and  $$\Delta AED$$   are similar. The length of AC is 6 units. #17

• Dilate triangle ABC using center A by a scale factor of 1/2, then reflect over line AC

• Dilate triangle AED using center A by scale factor if 2, then reflect over line AC

• Reflect triangle ABC over line AC, then dilate using center A by a scale factor of 1/2

• Reflect triangle AED over line AC, then dilate using center A by a scale factor of 2

• Translate triangle AED by directed line segment DC, then dilate using center C by scale factor 2

Multiple Choice

Triangle ABC was dilated and translated to form a similar triangle A'B'C'. #18

• $$\frac{1}{5}$$  

• $$\frac{2}{5}$$  

• $$\frac{5}{2}$$  

• $$\frac{5}{1}$$  

Multiple Choice

Choose the statement that accurately describes the relationship between ABCD and EFGH. #20

• ABCD and EFGH are congruent, but not similar.

• ABCD and EFGH are similar, but not congruent.

• ABCD and EFGH are both congruent and similar.

• ABCD and EFGH are neither congruent, nor similar.

Multiple Choice

Triangle ABC with Vertices A(-1, 2), B(-1, -2), and C(-4, -2) is dilated by a scale factor of 2 to form triangle A’B’C’. #24

What is the length in units, of side A’B’?

• 4

• 2

• 8

• 7

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Multiple Choice

Are the following similar? Why or why not? #27

• Yes, they are both trapezoids

• No, they have different sizes

• No, the ratios of the corresponding sides are not equal.

• Yes, they have the same base and 4 angles

Multiple Choice

What is the scale factor from MNOP to ABCD? #30

• 2/3

• 1/2

• 3/2

• 2