This document provides instruction on determining if two figures are similar using transformations. It includes examples of determining if figures are similar by checking if corresponding angles are congruent and if corresponding sides are proportional. It also covers finding missing measures in similar figures using scale factors and proportions. Determining similarity involves rotations, reflections, translations, and dilations, while congruence only involves rigid motions.

1. Course 3, Lesson 7-4
Determine if the two figures are similar by using transformations.
Explain your reasoning.
1.
2.
3. What type of transformation produces a figure that is not congruent
to the original figure?

2. Course 3, Lesson 7-4
ANSWERS
1. yes; Sample answer: A dilation and a translation maps figure MNOP
onto figure ABCD.
2. no; Sample answer: The ratio of the side lengths are not equal.
3. dilation

3. HOW can you determine
congruence and similarity?
Geometry
Course 3, Lesson 7-4

4. Course 3, Lesson 7-4 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
• 8.G.4
Understand that a two-dimensional figure is similar to another if the
second can be obtained from the first by a sequence of rotations,
reflections, translations, and dilations.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Geometry

5. To
• use corresponding angles and sides
to determine similarity,
• find missing measures in two
similar figures
Course 3, Lesson 7-4
Geometry

6. • similar polygons
• scale factor
Symbols
• is similar to
Course 3, Lesson 7-4
Geometry

7. Course 3, Lesson 7-4
Geometry
Words If two polygons are similar, then
• their corresponding angles are congruent and
• the measures of their corresponding sides are proportional.
Model
Symbols , , ,
AB BC AC
A X B Y C Z
XY YZ XZ
          and

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. Determine whether
rectangle HJKL is
similar to rectangle
MNPQ. Explain.
First, check to see if corresponding
angles are congruent.
Since the two polygons are rectangles, all of their angles are right
angles. Therefore, all corresponding angles are congruent.
Next, check to see if corresponding sides are proportional.
Since and are not equivalent, the rectangles are not similar.

9. Answer
Need Another Example?
Determine whether triangle DEF is similar to
triangle HJK. Explain.
Yes; the corresponding angles are
congruent and

10. 1
Need Another Example?
2 3
Step-by-Step Example
2. Quadrilateral WXYZ is similar to quadrilateral ABCD.
a.
Find the scale factor from quadrilateral
ABCD to quadrilateral WXYZ.
So, a length on polygon WXYZ is times
as long as the corresponding length on
polygon ABCD. Let m represent the
measure of XY.
Set up a proportion to find the
missing measure.
a. Describe the transformations that map
WXYZ onto ABCD.
b. Find the missing measure.
Since the figures are similar, they are not the same size. Choose two
corresponding sides and determine what transformations will map one
onto the other. A translation followed by a dilation will map AB onto WX.
b.
scale factor: = or
m = (12) Write the equation.
Multiply.
Write the proportion.
XY = m, BC = 12, YZ = 15,
CD = 10
Find the cross products.
Simplify.
Division Property of Equality
m • 10 = 12 • 15
10m = 180
m = 18
m = 18

11. Answer
Need Another Example?
Rectangle LMNO is similar to rectangle GHIJ.
a. Describe the transformations that map GHIJ onto LMNO.
b. Find the missing measure.
a. Since the figures are similar, they are
not the same size. The transformation
is a translation and a dilation.
b. 6

12. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-4
Geometry

13. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-4
Geometry
Sample answer:
• If two polygons have corresponding angles that are
congruent and corresponding sides that are
proportional, then they are similar.

14. A rectangle has a length of
10 feet and a height of 12 feet.
Another rectangle that is
similar to the first has a length
of 15 feet. What is the height
of the second rectangle?
Course 3, Lesson 7-4
Ratios and Proportional RelationshipsFunctionsGeometry