Congruence Transformations (4.7) Check.1.7 Recognize the capabilities and the limitations of calculators and computers in solving problems. Check.4.31 Use properties of single transformations and compositions of transformations to determine their effect on geometric figures (e.g. reflections across lines of symmetry, rotations, translations, glide reflections, and dilations). Check.4.34 Create and analyze geometric designs using rigid motions (compositions of reflections, translations, and rotations). CLE Establish processes for determining congruence and similarity of figures, especially as related to scale factor, contextual applications, and transformations.

Working in teams Complete Transforming Fish Activity

Mrs. Motlow Classroom Procedures Absence 1. Go to Assignment Notebook or Website to find work completed while you were out. 2. All make up work is due within 5 days of absence. 4. If you are aware of an upcoming absence, let me know, and I will provide you assignments in advance. You are responsible for anything covered while you were out. 3. Clearly mark Make-up Work including dates missed and turn into box for grading.

transformation congruence transformation preimage Image reflection translation rotation

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 (x, y )  (x + 5, y – 2) (-2, 4)  (-2 + 5, 4 - 2) (-2, 4)  (3, 2) (-1, 1)  (-1 + 5, 1 – 2)  (4, – 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. Point of Rotation

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. Line of reflection

A.reflection B.translation C.rotation D.none of these A. Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Example 1B A.reflection B.translation C.rotation D.none of these B. Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Example 1C A.reflection B.translation C.rotation D.none of these C. Identify the type of congruence transformation shown as a reflection, translation, or rotation.

Identify a Real-World Transformation 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.

A.reflection B.translation C.rotation D.none of these GAME Identify the type of congruence transformation shown by the image of the chess piece as a reflection, translation, or rotation.

Verify Congruence after a Transformation Triangle ABC with vertices A(–1, –4), B(–4, –1), and C(–1, –1) is a transformation of ΔXYZ with vertices X(–1, 4), Y(–4, 1), and Z(–1, 1). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. A. B. C. D.

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. By SSS, ΔJKL  ΔPQR

Practice Assignment Page – 30 Even

8. Translation or reflection 10. Rotation 12. reflection, rotation or translation 14. Reflection 16. Translation 18. ABC is translation 20. XYZ is a rotation 22. Translation and rotation 24. Rotation 26. Translation 28. Vertical, A, H, I, M, O, T, U, V, W, X, Y Horizontal B, C, D, E, H, I, K, O, X