Lesson 4-7 Congruence Transformations TARGETS ID reflections, translations, and rotations. Verify congruence after congruence transformation. Targets

Types of transformations LESSON 4-7: Congruence Transformations Translation or “slide” moves all the pts the same distance & in the same direction Preimage: original figure Reflection or “flip” over a line called the line of reflection Rotation or “turn” around a fixed point called the center of rotation Types of transformations

LESSON 4-7: Congruence Transformations EXAMPLE 1 & 2 Identify Congruence Transformations Identify the type of congruence transformation shown as a reflection, translation, or rotation. reflection translation translation rotation translation reflection rotation reflection Example 1 & 2

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. Example 3

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. 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. Example 3

Verify Congruence after a Transformation Example 3

Answer: By SSS, ΔJKL  ΔPQR. 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. Example 3

4-7 Word Problem Practice LESSON 4-7 & 4-8: Geometric Transformations Homework Pg 297-300 #7-16, 19, 20 & 4-7 Word Problem Practice Homework