• ID reflections, translations, and rotations.

• Verify congruence after congruence transformation.

Lesson 4-7 Congruence Transformations

TARGETS

LESSON 4-7: Congruence Transformations

QuickTime™ and a decompressor

are needed to see this picture.

Rotation or “turn” arounda fixed point called thecenter of rotation

Translation or “slide” moves all the pts the same distance & in the same direction

Reflection or “flip” overa line called the line ofreflection

Preimage: original figure

Identify Congruence TransformationsIdentify the type of congruence transformation shown as a reflection, translation, or rotation.

EXAMPLE 1 & 2

LESSON 4-7: Congruence Transformations

translation rotation reflection translation

reflection rotation reflection translation

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.

EXAMPLE 1 & 2

LESSON 4-7: Congruence Transformations

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.

EXAMPLE 1 & 2

LESSON 4-7: Congruence Transformations

Verify Congruence after a Transformation

Solve Graph each figure. The transformationappears to be a translation 6 units rightand 2 units up. Find the measures of thesides 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 compareeach side of the triangles. The sides are congruent, so the triangles arecongruent.

LESSON 4-7 & 4-8: Geometric Transformations

Homework

Pg 297-300 #7-16, 19, 20&

4-7 Word Problem Practice