Transcript 4.7 Congruence Transformations
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 QuickTime™ and a decompressor are needed to see this picture.
Reflection or “flip” over a line called the
line of reflection
Preimage: original figure 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.
Solve Verify Congruence after a Transformation
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, Δ
JKL
Δ
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.
LESSON 4-7 & 4-8: Geometric Transformations