This document provides instruction and examples for determining congruence and similarity using transformations. It explains that two figures are similar if one can be obtained from the other by a sequence of rotations, reflections, translations, and dilations. Examples show using transformations and writing side ratios to determine if figures are similar. The last example finds the dimensions of an image that is enlarged twice by different scale factors, showing the results are similar.

1. Course 3, Lesson 7-3
Use the draw a diagram strategy to solve Exercises 1 and 2.
1. Jack framed a family portrait. The portrait was eight inches wide
and ten inches long. He put a border around the portrait that was
three inches wide. What was the length and width of the frame
he needed for the portrait and border?
2. A grandmother has five grandchildren, Joe, Kim, Wally, Sam,
and Anna. Wally is neither the oldest nor the youngest. Anna is
younger than Kim, who is older than Wally. Joe is older than Kim
and Sam. Sam is the youngest boy and is older than Anna. Who
is the oldest grandchild?

2. Course 3, Lesson 7-3
ANSWERS
1. 14 inches wide and 16 inches long
2. Joe

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

4. Course 3, Lesson 7-3 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.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.
Geometry

5. To
• determine similarity of two figures
using transformations,
• use the scale factor to find missing
side lengths of similar figures
Course 3, Lesson 7-3
Geometry

6. • similar
Course 3, Lesson 7-3
Geometry

7. Translate DEF down 2 units and 5 units to the right so
D maps onto G.
1
Need Another Example?
2
3
Step-by-Step Example
1. Determine if the two
triangles are similar by
using transformations.
Since the orientation of the figures is the same, one of the
transformations is a translation.
Write ratios comparing the lengths of each side.
4 Since the ratios are equal, HGI is the dilated image of EDF. So,
the two triangles are similar because a translation and a dilation maps
EDF onto HGI.

8. Answer
Need Another Example?
Determine if the two triangles are similar using
transformations.
no; Sample answer: The ratio of the side lengths
are not equal for all of the
sides.
= , while =

9. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Determine if the two
rectangles are similar by
using transformations.
The orientation of the figures
is the same, so one of the
transformations might be a
rotation.
Rotate rectangle VWTU 90° clockwise about W so
that it is oriented the same way as rectangle WXYZ.
Write ratios comparing the lengths of each side.
The ratios are not equal. So, the two rectangles are not similar
since a dilation did not occur.

10. Answer
Need Another Example?
Determine if the two rectangles are similar
using transformations.
yes; Sample answer: a rotation
and a dilation with a scale factor
of maps rectangle HIJK onto
rectangle MNLO.

11. 1
Need Another Example?
2
3
Step-by-Step Example
3. Ken enlarges a photo by a scale factor of 2 for his webpage. He then
enlarges the webpage photo by a scale factor of 1.5 to print. If the
original photo is 2 inches by 3 inches, what are the dimensions of the
print? Are the enlarged photos similar to the original?
Multiply each dimension of the original photo by 2 to find the
dimensions of the webpage photo.
So, the webpage photo will be 4 inches by 6 inches. Multiply the
dimensions of that photo by 1.5 to find the dimensions of the print.
The printed photo will be 6 inches by 9 inches. All three photos
are similar since each enlargement was the result of a dilation.
2 in. × 2 = 4 in. 3 in. × 2 = 6 in.
4 in. × 1.5 = 6 in. 6 in. × 1.5 = 9 in.

12. Answer
Need Another Example?
A baker is reducing an 8-inch by 10-inch photo to place
the image on a cake. He reduces it by a scale factor of
0.8. Then decides the image is still too large, and
reduces it by a scale factor of 0.9. What are
the dimensions of the final image? Is the reduced
image similar to the original?
5.76 in. × 7.2 in.; yes

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

14. How did what you learned
today help you answer the
HOW can you determine
congruence and similarity?
Course 3, Lesson 7-3
Geometry
Sample answers:
• Two figures are similar if one is the result of a
sequence of transformations and dilations.
• Similar figures have the same shape. Because of the
dilation, the sizes of the figures may be different.

15. A figure is dilated by a scale factor
of a and then the image is dilated
by a scale factor of b. Is the result
the same if the figure is first dilated
by the scale factor b and then by the
scale factor a? Explain.
Course 3, Lesson 7-3
Ratios and Proportional RelationshipsFunctionsGeometry