Lesson 8-6.6

Lesson 6.6

Dilations and Similarity

By Reed Carbone

Definitions:

Dilation: A Transformation that either enlarges or shrinks a figure based on a fixed point. A dilation multiplies all the sides of a figure by a fixed number.

Scale Factor: A scale factor or "r" is the ratio of the length of the pre-image and the new-image. (It is the number you multiply by to get your new figure.) It is found by finding a ratio of the "new" side to the "old" side or "new over old".

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Definitions:

Enlargement: An enlargement is a dilation that makes your figure bigger. The scale factor "r" must be greater than 1. ( r > 1)

Reduction: A reduction is a dilation that makes a figure smaller. The scale factor "r" must be less than 1 but greater than 0. (0 < r < 1)

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Definitions:

Similar: We say figures are similar if they are proportional to each other. Meaning if you can dilate a figure to get a different figure, these figures would be similar.

Congruent: We say figures are congruent if they are the same as one another. Any rotation, reflection or translation will produce a congruent figure.

Subject | Subject

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​Visual:

Multiple Choice

These figures are:

• Similar

• Congruent

• Both similar and congruent

• Neither similar nor congruent

Multiple Choice

These two triangles are:

• Similar

• Congruent

• Both similar and congruent

• Neither similar nor congruent

Multiple Choice

These three shapes are:

• Similar

• Congruent

• Both similar and congruent

• Neither similar nor congruent

​Perform a dilation on the line where the scale factor is 2.

​Perform a dilation of the figure with scale factor 1/2 and center (0,0)

Multiple Choice

Which of these answers shows a dilation?

How to find the scale factor:

Multiple Choice

What is the scale factor in this image?

• 1/3

• 6

• 3

• 9

Multiple Choice

What are the two types of dilations?

• Enlargement and Reduction

• Reflection and Rotation

• Slide and Translation

• Bigger and Smaller

Multiple Choice

What is the scale factor in this dilation?

• 2

• 1

• 1/2

• 1/4

Conclusion: Two complete sentences about what we learned.