MODULE
STUDY GUIDE REVIEW
Congruent Figures
Essential Question: How can you use congruency to solve
real-world problems?
KEY EXAMPLE
18
(Lesson 18.1)
Write the vertices of the image of the figure given by
A (2, 1), B (3, 3), C (2, 4) after the transformations.
(x, y) → (x + 1, y + 2) → (3x, y)
A (2, 1) → A' (3, 3)
B (3, 3) → B' (4, 5)
Apply the transformations in
order to each point. Apply the first
transformation.
A' (3, 3) → A" (9, 3)
Apply the second transformation.
C (2, 4) → C' (3, 6)
B' (4, 5) → B" (12, 5)
C' (3, 6) → C" (9, 6)
The image of the transformed figure is determined by the points
A" (9, 3), B" (12, 5), C" (9, 6).
KEY EXAMPLE
(Lesson 18.2)
Determine whether a triangle △ABC is congruent to its image after the transformations
(x, y) → (x + 1, y + 2) → (2x, y).
The transformation (x, y) → (x + 1, y + 2) is a translation, which is a rigid motion, so after this
transformation the image is congruent. The transformation (x, y) → (2x, y) is a dilation, which is not
a rigid motion, so the image from this transformation is not congruent.
After the transformations, the image is not congruent to △ABC because one of the transformations
is not a rigid motion.
KEY EXAMPLE
(Lesson 18.3)
Find the angle in △DFE congruent to ∠A and the side congruent to ¯
BC when
△ABC ≅ △DFE.
Since_
△ABC
_≅ △DFE, and corresponding parts of congruent figures are congruent, ∠A ≅ ∠D
and BC ≅ FE.
Module 18
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Study Guide Review
EXERCISES
Write the vertices of the image of the figure after the transformations. (Lesson 18.1)
1.
The figure given by A(1, -2), B(2, 5), C(-3, 7), and the transformations
(x, y) → (x, y - 1) → (-y, 2x)
.
Find the rigid motions to transform one figure into its congruent figure. (Lesson 18.2)
F
2. In the figure, △ABC ≅ △DEF.
The rigid motions to transform from △ABC to △DEF are
E
D
.
Find the congruent parts. (Lesson 18.3)
-8
3. Given △ABC ≅ △DEF, ∠A ≅
.
_
4. Given △ABC ≅ △DEF, CA ≅
.
-4
8
y
B
4 A
C
x
0
-4
4
8
-8
MODULE PERFORMANCE TASK
Jigsaw Puzzle
A popular pastime, jigsaw puzzles are analogous to the series of
transformations that can be performed to move one figure onto another
congruent figure.
© Houghton Mifflin Harcourt Publishing Company • Image Credits:
©Hitdelight/Shutterstock
In the photo, identify at least three pieces that would likely fit into one of the
empty spaces in the puzzle. Describe the rotations and translations necessary
to move the piece to its correct position in the puzzle.
Module 18
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Study Guide Review
Ready to Go On?
18.1–18.3 Congruent Figures
• Online Homework
• Hints and Help
• Extra Practice
Predict the results of the transformations. (Lesson 18.1)
1. Triangle △ABC is in the first quadrant and translated along ⟨2, 1⟩ and reflected across the x-axis.
Which quadrant will the triangle be in after the first transformation?
Which quadrant will the triangle be in after the second transformation?
Determine whether the triangles are congruent using rigid motions. (Lesson 18.2)
2. Using the graph with △ABC, △DEF, and △PQR:
A. Determine whether △ABC is congruent to △DEF.
F 4 y
E
-4
B. Determine whether △DEF is congruent to △PQR.
R
D
-2
P
B
2
0
-2
A
2
Cx
4
Q
Find the congruent parts of the triangles. (Lesson 18.3)
© Houghton Mifflin Harcourt Publishing Company
3. List all of the pairs of congruent sides for two congruent triangles △ABC and △DEF.
ESSENTIAL QUESTION
4. How can you determine whether a figure is congruent to another figure?
Module 18
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Study Guide Review
MODULE 18
MIXED REVIEW
Assessment Readiness
1. A line segment with points R(3, 5) and S(5, 5) is reflected across the line y = -x and
translated 2 units down. Determine whether each choice is a coordinate of the image
of the line segment. Select Yes or No for A–C.
A. R' (-5, -3)
Yes
No
B. R' (-5, -5)
C. S' (-5, -7)
Yes
Yes
No
No
2. The polygon ABCD is congruent to PQRS. The measure of angle B is equal to 65°. Choose
True or False for each statement.
A. The supplement of angle Q measures 115°.
True
False
B. Angle Q measures 115°.
True
False
C. The supplement of angle B measures 115°.
True
False
3. Triangle LMN is a right triangle. The measure of angle L is equal to 35°. Triangle LMN is
congruent to △PRQ with right angle R. Choose True or False for each statement.
A. The measure of angle Q is 55°.
True
False
B. The measure of angle R is 90°.
True
False
C. The measure of angle P is 35°.
True
False
Module 18
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Study Guide Review
© Houghton Mifflin Harcourt Publishing Company
_
4. The two triangles, △ABC and
△DEF,
are
congruent.
Which
side
is
congruent
to
CA
?
_
Which side is congruent to BA?