Navigation

9-12 Integrated Math 2 Unit 2 Lesson 6

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 •Integrated Math 2 Integrated Math 3

Unit

Unit 1 •Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

Modeling Prompts

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 •Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18

Lesson | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

©2024 Illustrative Mathematics®. Licensed under CC BY-NC 4.0.

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

family

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 2, Lesson 6

Connecting Similarity and Transformations

$Course Icon$

Integrated Math 2

Practice

Problem 1

Student Task Statement

Find a sequence of rigid motions and dilations that takes square to square .

<p>Squares A B C D and E F G H. A B C D has A upper left, base B C and left side A B is 5. E F G H has G above E, rests on E and right lower side E F is 2.</p>

to access Practice Problem Solutions.

Problem 2

Student Task Statement

Quadrilaterals and are similar.

What is the scale factor of the dilation that takes to ?
What is the scale factor of the dilation that takes to ?

<p>Quadrilaterals P and Q are similar. P has sides from the top measuring 4, 3 and 2, Q has sides from the top 5, none and 2 point 5. </p>

to access Practice Problem Solutions.

Problem 3

Student Task Statement

What is our definition of “similarity”?

If two figures have the same angles, then they are similar.
If two figures have proportional side lengths, then they are similar.
If there is a sequence of rigid transformations taking one figure to another, then they are similar.
If there is a sequence of rigid transformations and dilations that take one figure to the other, then they are similar.

to access Practice Problem Solutions.

Problem 4

ForLesson 5: Splitting Triangle Sides with Dilation (Part 1)

Student Task Statement

Triangle is formed by connecting the midpoints of the sides of triangle . The lengths of the sides of are shown. What is the length of ?

<p>Triangles A B C and D E F. D is the midpoint of segment A B. E is the midpoint of segment B C. F is the midpoint of segment A C. Line D E has length 2, Line E F has length 3, Line D F has line 4.<br>
</p>

3 units
4 units
6 units
8 units

to access Practice Problem Solutions.

Problem 5

ForLesson 5: Splitting Triangle Sides with Dilation (Part 1)

Student Task Statement

If is 12, what is the length of ?

<p>Triangle A B C with segment A’ B’ drawn. A A’ is 2 and A’ C is 4. B B’ is 3 and B’ C is 6. Angle B is 40 degrees.</p>

to access Practice Problem Solutions.

Problem 6

ForLesson 4: Dilating Lines and Angles

Student Task Statement

Right angle is taken by a dilation with center and a scale factor of to angle . What is the measure of angle ?

to access Practice Problem Solutions.

Problem 7

ForLesson 4: Dilating Lines and Angles

Student Task Statement

Dilate point using center and scale factor .
Dilate segment using center and scale factor .

<p>Segments C D and B D intersect at point D. Point A lies on segment B D between B and D.</p>

to access Practice Problem Solutions.

Problem 8

ForLesson 3: Measuring Dilations

Student Task Statement

A polygon has perimeter 12. It is dilated with a scale factor of , and the resulting image has a perimeter of 8. What is the scale factor?

to access Practice Problem Solutions.

Problem 9

ForLesson 13: Proofs about Parallelograms

Student Task Statement

Select all the statements that must be true.

Parallelograms have four congruent sides.
Both sets of opposite sides of a parallelogram are parallel and congruent.
A trapezoid is a parallelogram.
Diagonals of a parallelogram bisect each other.
Diagonals of a parallelogram are congruent.

to access Practice Problem Solutions.

Lesson 6 Resources

Student Materials