1.05 Similar Figures (Dilations)

1.05 Similar Figures (Dilations)

​Dilation:

A type of transformation that changes the size but not the shape of a figure.

​SCALE FACTOR

​​In order to define how much a pre-image has changed in a dilation, we use the scale factor.

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A scale factor that is a number greater than 1 represents a dilation that increases the size of the pre-image.

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A scale factor that is less than 1 represents a decrease in the size of the pre-image.

​Scale factor:

A ratio of two corresponding lengths that determines the change in size from a pre-image to an image

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​(Can also be found by dividing the new coordinates by the old coordinates.)

Multiple Choice

Triangle FLA is shown on the coordinate plane:

Find the coordinates of triangle F'L'A' if the pre-image is transformed by a scale factor of 2.

• F' (−6, −4)

  L' (−6, −2)

  A' (−4, −4)

• F' (6, 4)

  L' (6, 2)

  A' (4, 4)

• F' (−1.5, −1)

  L' (−1.5, −.5)

  A' (−1, −1)

• F' (1.5, 1)

  L' (1.5, .5)

  A' (1, 1)

Multiple Choice

Find the coordinates of polygon A'B'C'D' if the pre-image is transformed by a scale factor of

1/2.

• A' (4, 8)

  B' (4, 0)

  C' (8, 0)

  D' (8, 8)

• A' (-1, -2)

  B' (-1, 0)

  C' (-2, 0)

  D' (-2, -2)

• A' (1, 2)

  B' (1, 0)

  C' (2, 0)

  D' (2, 2)

• A' (-4, -8)

  B' (-4, 0)

  C' (-8, 0)

  D' (-8, -8)

​Triangle R' was created using a dilation of triangle R. Identify the scale factor.

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​To find the scale factor, choose two sides that are corresponding or in the same position on the triangle. Set up a ratio with the image measurement on top and the pre-image measurement in the denominator.

Put the value of the image in the numerator and the pre-image in the denominator.

​

​

​Finding Scale Factor not on the Coordinate Plane

​Finding Scale Factor on the Coordinate Plane

Fill in the Blanks

Triangle ABC has been dilated to create triangle A'B'C'. Find the scale factor.

​Having the same shape and angle measure but different sizes; expressed with the symbol ∼.

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​ angles correspond to one another and are congruent

• sides correspond to one another and are proportional

• sides all have the same proportional relationship

​Similar Figures

​Similar vs Congruent

​Note! Congruent figures also qualify as similar. They have the same angle measurements and are the same size. When figures are marked as congruent, you can also assume that they are similar.

Multiple Choice

Which of the following sets of figures are not ONLY similar?

​Putting it all together...

​You have learned about four types of transformations: translations (slide), rotations (spin), reflections (flip), and dilations (change in size).

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Remember that translations, rotations, and reflections create congruent figures.

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Dilations create similar figures.

Open Ended

Triangle X''Y''Z'' was created using a sequence of transformations. Describe the sequence of transformations. Is triangle XYZ similar or congruent to triangle X''Y''Z''?

Multiple Choice

What would the final coordinates be of A"B"D"E" if polygon ABDE is dilated with a scale factor of 1/2

and reflected over the x-axis?

•  A" (-1, 3)

   B" (-1, 1)

   D" (-2, 0)      

   E" (-3, 2)

•  A" (1, −3)

   B" (1, −1)

   D" (2, 0)      

   E" (3, −2)

•  A" (4, −8)

   B" (4, −4)

   D" (8, 0)      

   E" (12, −8)

•  A" (-4, 8)

   B" (-4, 4)

   D" (-8, 0)      

   E" (-12, 8)

​Lesson Summary

Dilation: A type of transformation that changes the size but not the shape of a figure.

Scale factor: A ratio of two corresponding lengths that determines the change in size from a pre-image to an image.

Similar: Having the same shape and angle measure but different sizes; expressed with the symbol ∼.

Dilation is a type of transformation that involves making a figure larger or smaller. The scale factor is the number by which each side or coordinate is multiplied to change the size of the pre-image. Dilated figures are similar but not congruent.

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Similar figures have the same angle measurements and ratio of sides, but can be different sizes. Congruent figures are exactly the same size and shape.

​To Do:

​Ensure you have completed 1.01 - 1.05 in Canvas. (1.01-1.07 by 8/30)

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​If you are stuck due to a failing quiz, send me corrections for your last failed attempt. I will review them and then unlock an additional attempt.

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​If you need help, message me or use the appointment link to schedule a one-on-one meeting.

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​Join me on Wednesday 9:30AM-10AM if you have any questions from 1.01-1.07. (Meeting link posted in TEAMS under module 1.)