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**Lesson 4 – 7 Congruence Transformations**

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

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**Transformations Transformations –**

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

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**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.

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**Types of Congruence Transformations**

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

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**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

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**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.

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**Rotation Reflection Translation**

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

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**Translation Rotation Reflection**

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

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

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**Translation Reflection**

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

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**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…

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**Verify the triangles are congruent**

Since no angles are known we will prove congruence by SSS.

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

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