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Dilations & Similarity

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# Dilations & Similarity - PowerPoint PPT Presentation

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

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 ____________________.

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!
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.

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.

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?

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.

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?

Practice

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