• Transformation is an operation
that maps an original
geometric figure (called a
preimage), onto a new figure
(called the image).
• A congruence transformation
(also called a rigid
transformation or an isometry)
is a transformation that creates
an image that is congruent to
the preimage
• Reflection
• Translation
• Rotation
Identify Congruence Transformations
A. Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
Each vertex and its image
are in the same position, just
5 units right and 2 units down.
Answer: This is a translation.
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.
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.
A. Identify the type of
congruence transformation
shown as a reflection,
translation, or rotation.
A. reflection
B. translation
C. rotation
0%
D
0%
C
0%
B
A
D. none of these
0%
A.
B.
C.
D.
A
B
C
D
B. Identify the type of
congruence transformation
shown as a reflection,
translation, or rotation.
A. reflection
B. translation
C. rotation
0%
D
0%
C
0%
B
A
D. none of these
0%
A.
B.
C.
D.
A
B
C
D
C. Identify the type of
congruence transformation
shown as a reflection,
translation, or rotation.
A. reflection
B. translation
C. rotation
0%
D
0%
C
0%
B
A
D. none of these
0%
A.
B.
C.
D.
A
B
C
D
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.
B. translation
C. rotation
0%
B
D. none of these
A
0%
A.
B.
C.
D.
A
B
C
D
D
A. reflection
C
GAME Identify the type
of congruence
transformation shown by
the image of the chess
piece as a reflection,
translation, or rotation.
0%
0%
Verify Congruence after a Transformation
Triangle PQR with vertices P(4, 2), Q(3, –3), and
R(5, –2) is a transformation of ΔJKL 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
transformation—reflection, 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.
Verify Congruence after a Transformation
Solve
Graph each figure. The transformation
appears to be a translation 6 units right
and 2 units up. Find the measures of the
sides of each triangle.
Triangle ABC with vertices A(–1, –4),
B(–4, –1), and C(–1, –1) is a
transformation of ΔXYZ 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.
0%
A
D.
0%
0%
0%
D
C.
A
B
C
D
C
B.
B
A.
A.
B.
C.
D.