Splash Screen

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Splash Screen
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Lesson Menu
Five-Minute Check (over Lesson 46) Then/Now New
Vocabulary Key Concept Reflections,
Translations, and Rotations Example 1 Identify
Congruence Transformations Example 2 Real-World
Example Identify a Real-World Transformation Exam
ple 3 Verify Congruence after a Transformation
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5-Minute Check 1
Name two congruent segments if ?1 ? ?2.

• A
• B
• C
• D

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5-Minute Check 2
A. ?R ? ?W B. ?S ? ?V C. ?S ? ?U D. ?S ? ?T

• A
• B
• C
• D

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5-Minute Check 3
Find m? R if m? RUV 65.
A. 30 B. 40 C. 50 D. 60

• A
• B
• C
• D

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5-Minute Check 4
A. 45 B. 55 C. 70 D. 110

• A
• B
• C
• D

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5-Minute Check 5
Find x if ?LMN is equilateral with LM 2x 4,
MN x 6, and LN 3x 14.
A. 20 B. 10 C. 5 D. 2

• A
• B
• C
• D

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5-Minute Check 6
In the isosceles triangle BCD, ?C is the vertex
angle. Which sides are congruent?

• A
• B
• C
• D

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Then/Now
You proved whether two triangles were congruent.
(Lessons 43, 44, and 45)

• Identify reflections, translations, and rotations.

• Verify congruence after congruence transformation.

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Vocabulary

• Transformation given a triangle (or other
  shape) a change in size or shape that creates a
  new shape
• congruence transformation a transformation that
  does not change the size of the shape
• Preimage the original shape
• Image the new shape created by a transformation
• Isometry a congruence transformation

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Concept
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Example 1
Identify Congruence Transformations
A. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
Each vertex and its imageare in the same
position, just5 units right and 2 units down.
Answer This is a translation.
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Example 1
Identify Congruence Transformations
B. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
Each vertex and its image are the same distance
from the origin. The angles formed by each pair
of corresponding points and the origin are
congruent.
Answer This is a rotation.
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Example 1
Identify Congruence Transformations
C. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
Each vertex and its image are the same distance
from the x-axis.
Answer This is a reflection.
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Example 1A
A. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
A. reflection B. translation C. rotation D. none
of these

• A
• B
• C
• D

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Example 1B
B. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
A. reflection B. translation C. rotation D. none
of these

• A
• B
• C
• D

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Example 1C
C. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
A. reflection B. translation C. rotation D. none
of these

• A
• B
• C
• D

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Example 2
Identify a Real-World Transformation
BRIDGES Identify the type of congruence
transformation shown by the image of the bridge
in the river as a reflection, translation, or
rotation.
Answer The image is a reflection, with the line
at which the bridge meets the water as the line
of reflection.
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Example 2
GAME Identify the type of congruence
transformation shown by the image of the chess
piece as a reflection, translation, or rotation.
A. reflection B. translation C. rotation D. none
of these

• A
• B
• C
• D

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Example 3
Verify Congruence after a Transformation
Triangle PQR with vertices P(4, 2), Q(3, 3), and
R(5, 2) is a transformation of ?JKL with
vertices J(2, 0), K(3, 5), and L(1, 4).
Graph the original figure and its image. Identify
the transformation and verify that it is a
congruence transformation. Understand You are
asked to identify the type of transformationrefl
ection, translation, or rotation. Then, you need
to show that the two figures are congruent. Plan
Use the Distance Formula to find the measure
of each side. Then show that the two triangles
are congruent by SSS.
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Example 3
Verify Congruence after a Transformation
Solve Graph each figure. The transformation appea
rs to be a translation 6 units right and 2 units
up. Find the measures of the sides of each
triangle.
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Example 3
Verify Congruence after a Transformation
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Example 3
Verify Congruence after a Transformation
Answer By SSS, ?JKL ? ?PQR. Check Use the
definition of a translation. Use a ruler to
measure and compare each side of the triangles.
The sides are congruent, so the triangles
are congruent.
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Example 3
Triangle ABC with vertices A(1, 4), B(4, 1),
and C(1, 1) is a transformation of ?XYZ with
vertices X(1, 4), Y(4, 1), and Z(1, 1). Graph
the original figure and its image. Identify the
transformation and verify that it is a congruence
transformation.

• A
• B
• C
• D

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• Homework p 298 7-16