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http://contentstore.ple.platoweb.com/content/GeoGebra.v5.0/A3.2_Similarity_Transformations.html

Question 1

Determine the sequences of rigid motions and dilations that map the preimageABCDEto each of its images.If no sequence of rigid motions and dilations mapsABCDEonto an image, state that in the table.Remember to describe each transformation completely.For example, you must specify a line of reflection for each reflection and a center of dilation for each dilation.Perform the transformations in GeoGebra to check your responses.

Image Sequence of Rigid Motions and Dilations

FGHIJ

KLMNP

QRSTU

VWXYZ

Question 2

Based on your work with similarity transformations in question 1, which images are similar to the preimageABCDE?Which images are not similar?

Question 3

Often, there is more than one set of sequences that will take a preimage to an image.Determine one or two other sequences to createFGHIJfromABCDE.

Image Sequence of Rigid Motions and Dilations

FGHIJ

FGHIJ

Question 4

Calculate the lengths of the corresponding sides forFGHIJandABCDE.You will need to use the distance formula,d=(x2x1)2+(y2y1)2

, for sides that are not purely horizontal or vertical.Show your work in the table.Afterward, confirm your calculations using GeoGebra.

Side Calculation Using GeoGebra

AB

FG

BC

GH

CD

HI

DE

IJ

EA

JK

Question 5

What is the ratio of the side lengths on polygonFGHIJto the corresponding side lengths on polygonABCDE?Enter the ratio in the table.How does this ratio relate to the scale factor of the dilation?

Side Lengths Ratio

FG:AB

GH:BC

HI:CD

IJ:DE

JF:EA

Question 6

Based on your work in questions 1 through 5, what is a similarity transformation?What is necessary to determine whether two or more shapes are similar?Explain in terms of rigid transformations, dilations, proportionality, and scale factors.