Lesson 4-7 Congruence
Transformations
TARGETS
• ID reflections, translations, and rotations.
• Verify congruence after congruence
transformation.
LESSON 4-7: Congruence Transformations
Translation or “slide”
moves all the pts the
same distance & in the
same direction
Preimage: original figure
QuickTime™ and a
decompressor
are needed to see this picture.
Reflection or “flip” over
a line called the line of
reflection
Rotation or “turn” around
a fixed point called the
center of rotation
LESSON 4-7: Congruence Transformations
EXAMPLE 1 & 2
Identify Congruence Transformations
Identify the type of congruence transformation
shown as a reflection, translation, or rotation.
translation
reflection
rotation
rotation
reflection
reflection
translation
translation
LESSON 4-7: Congruence Transformations
EXAMPLE 1 & 2 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.
LESSON 4-7: Congruence Transformations
EXAMPLE 1 & 2 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.
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
Verify Congruence after a Transformation
Answer: By SSS, ΔJKL  ΔPQR.
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.
LESSON 4-7 & 4-8: Geometric Transformations
Homework
Pg 297-300 #7-16, 19, 20
&
4-7 Word Problem Practice