Similarity

Lesson 6

Let’s explore similar figures!

Equivalent Expressions

Warm Up

Use what you know about operations and their properties to write 3 expressions equivalent to the expression shown:

10(2 + 3)－8 • 3

Begin with Quiet Work Time. (2 min)

Discuss your thinking with a partner.

Which expressions �are you unsure about?

10(2 + 3)－8 • 3

Similarity Transformations (Part 1)

Activity 1

• Stronger and Clearer Each Time
• 5 Practices

similar

Two figures are similar if one can fit exactly over the other after rigid transformations and dilations.

In the figure, triangle ABC is similar to triangle DEF.

ABC was rotated around point B, then dilated with center point O.

Method 1: Dilate, Translate, Rotate, Reflect

• Dilate using D as the center with scale factor 2.
• Translate D to H.
• Rotate H as the center clockwise by 90 degrees.
• Reflect using the line that contains H and F.

Method 2: Reflect, Translate, Rotate, Dilate

• Reflect using the line that contains D and B.
• Translate D to H.
• Rotate using H as the center clockwise by 90 degrees.
• Dilate using H as the center with a scale factor 2.

Method 3: Translate, Rotate, Reflect, Dilate

• Translate B to F.
• Rotate using F as the center clockwise by 90 degrees.
• Reflect using the line the contains F and H.
• Dilate using F as the center with scale factor 2.

Please begin working!

Are you ready for more?

The same sequence of transformations takes Triangle A to Triangle B, takes Triangle B to Triangle C, and so on. Describe a sequence of transformations with this property.

Similarity Transformations

(Part 2)

Activity 2

• Compare and Connect

Sketch the resulting images similar to Figure A using the transformations given in the task.

A translation and a reflection.

Label your sketch Figure B.

A reflection and a dilation with scale factor greater than 1.

Label your sketch Figure C.

A rotation and a reflection.

Label your sketch Figure D.

A dilation with a scale factor less than 1 and a translation. Label your sketch Figure E.

Generally…

• Dilations create larger or smaller copies depending on the scale factor.
• Translations slide the first in a direction.
• Rotations “tilt” or “turn” the figure.
• Reflections change the “handedness” of a figure.

Methods for Translations and Dilations

Activity 3

• Clarify, Critique, Correct

similar

Remember:

Two figures are similar if there is a sequence of translations, rotations, and dilations that takes one figure to another!

Find at least one way to show that triangle ABC and DEF are similar using only the transformations given on your cards.

Please begin working as a team!

When showing two figures are similar, you can pick any point as the center of dilation if you know the scale factor because you can always adjust the position using a translation!

Two figures are similar if there is a sequence of translations, rotations, reflections, and dilations that maps one to another.

There’s more than one sequence of transformations that shows two figures are similar!

Today’s Goals

• I can apply a sequence of transformations to one figure to get a similar figure.
• I can use a sequence of transformation to explain why two figures are similar.

Showing Similarity

Cool Down