Lesson 4-7 Congruence
Transformation
Vocabulary
• Transformation-Is an operation that maps an
original geometric figure
• Preimage
• Image
• Congruence transformation-Is one which the
position of the image may differ from that of
the preimage, but the two figures remain
congruent
• Translation
• Isometry
• Rotation
• Reflection
Concept
Example 1
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.
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.
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.
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
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
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
Example
2 Transformation
Identify a Real-World
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.
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
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 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.
Example 3
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.
Verify Congruence after a Transformation
Example 3
Verify Congruence after a Transformation
Example 3
Answer:
By SSS, ΔJKL  ΔPQR.
• Transformations
• http://www.mathsisfun.com/geometry/transf
ormations.html