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Dilations & Similarity

Dilations & Similarity. Dilations Review. expansion. contraction. similar triangle. c ongruent angle. If the scale factor of a dilation is greater than 1, then it is a(n) ___________. If the scale factor of a dilation is less than 1, then it is a(n) ______________.

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Dilations & Similarity

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  1. Dilations & Similarity

  2. Dilations Review expansion contraction similar triangle congruent angle If the scale factor of a dilation is greater than 1, then it is a(n) ___________. If the scale factor of a dilation is less than 1, then it is a(n) ______________. A dilation maps any triangle to a _______________________. A dilation maps an angle to a ____________________.

  3. Scale Factor How do you find the scale factor? • image/preimage • 4/6 = 2/3 • Since the dilation is a contraction , the scale factor is a fraction. Ha!

  4. Extra Info Can a dilation be an isometry? ..only when the scale factor is equal to 1 In a dilation, the preimage and image are similar. For this reason, a dilation is an example of similarity mapping.

  5. What do you think these mean? A dilation D(n,C) maps any segment to a parallel segment times as long. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged.

  6. Dilation of a Rectangle If the scale factor is 2, what do you think the relationship would be between the perimeters and the areas of the rectangles?

  7. Dilation of a Rectangle Draw a dilation of a rectangle ABCD with vertices A(1,1), B(3,1), C(3,2) and D(1,2). Use the origin as the center and use a scale factor of 2.

  8. Dilation of a Rectangle 6:12 or 1:2 2:8 or 1:4 A dilation D(n,C) maps any polygon to a similar polygon whose area is n2 times as large. What is the ratio of the perimeters? What is the ratio of the areas?

  9. Practice OLD TEXTBOOK!!!!!!!!!!!!!!! Page 596 (2-14 even, 18-22 even)

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