In the geometry sketch below, quadrilateral ABCD is dilated about point E using the scale factor identified in the ScaleFactor slider bar. The resulting quadrilateral, A'B'C'D', is shown.

Interactive exercise. Assistance may be required.

Use the interactive geometry sketch to generate several different values, and then complete the table shown below.

Length of CD	Scale Factor	Length of CD × Scale Factor	Length of *C'D'*

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Length of CD	Scale Factor	Length of CD × Scale Factor	Length of *C'D'*
3.2	2.5	8	8
3.2	1.8	5.76	5.76
3.2	1.2	3.84	3.84
3.2	0.6	1.92	1.92

How are the length of CD, the Scale Factor, and the length of C'D' related?

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C'D' = CD × Scale Factor

Use the interactive geometry sketch to generate several different values, and then complete the table shown below.

Length of BC	Scale Factor	Length of BC × Scale Factor	Length of *B'C'*

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Length of BC	Scale Factor	Length of BC × Scale Factor	Length of *B'C'*
2.68	2.5	6.7	6.69
2.68	1.8	4.82	4.82
2.68	1.2	3.22	3.21
2.68	0.6	1.61	1.61

How are the length of BC, the Scale Factor, and the length of B'C' related?

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B'C' = BC × Scale Factor

Use the patterns that you have observed to predict the length of A'D' for the following scale factors:

Length of AD	Scale Factor	Length of *A'D'*
2	2.5
2	1.8
2	1.2
2	0.6

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Length of AD	Scale Factor	Length of *A'D'*
2	2.5	5
2	1.8	*3.6*
2	1.2	*2.4*
2	0.6	*1.2*

Practice

Trapezoid ABCD is similar to trapezoid HJKL. What is the length of KL?

Similar trapezoids with dimensions labeled

Use the grid below to record your answer. Type your answer in the boxes in front of and behind the decimal. Click inside each box to enter the numeral that belongs in the box, and then click the bubble beneath the numeral to shade the bubble that matches the numeral. After hitting the "Submit" button, incorrect portions of your answer will be shaded gray.

Interactive exercise. Assistance may be required.

Triangle JKE is similar to triangle PDG. What is the length of PD?

Similar triangles with dimensions labeled

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7 7 over 10 7 10 inches