Lesson 4 – 7 Congruence Transformations

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Presentation transcript:

Lesson 4 – 7 Congruence Transformations Geometry Lesson 4 – 7 Congruence Transformations Objective: Identify reflections, translations, and rotations. Verify congruence after a congruence transformation.

Transformations Transformations – An operation that maps an original figure (preimage) onto a new figure (image).

Congruence Transformations AKA rigid transformations AKA isometric (isometry) The position of the image may differ from that of the preimage, but the two figures remain congruent.

Types of Congruence Transformations Reflection A transformation over a line called the line of reflection. A flip over a line.

Types of Congruence Transformations Translation A transformation that moves all points of the original figure the same distance in the same direction. A slide of the points

Types of Congruence Transformations Rotation A transformation around a fixed point called the center of rotation. Each point of the original figure and it image are the same distance from the center. A turn about a point.

Rotation Reflection Translation Identify the type of congruence transformation shown as a reflection, translation, or rotation. Rotation Reflection Translation

Translation Rotation Reflection Identify the type of congruence transformation shown as a reflection, translation, or rotation. Translation Rotation Reflection

Identify the type of congruence transformation shown in the diagram as a reflection, translation, or rotation. Rotation

Translation Reflection Identify the type of congruence transformation shown in the diagram as a reflection, translation, or rotation. Translation Reflection

Verify Congruence after Transformation Triangle XZY with vertices X (2, -8), Z (6, -7), and Y(4, -2) is a transformation of Triangle ABC with vertices A (2, 8), B (6, 7), and C (4, 2). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. Reflection Cont…

Verify the triangles are congruent Since no angles are known we will prove congruence by SSS.

Homework Pg. 297 1 – 6 all, 8 – 28 E, 32, 38 – 42 E, 46 – 50 E