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Geometry

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 ).

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Geometry

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

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

  3. 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.

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

  5. 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

  6. 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.

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

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

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

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

  11. 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…

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

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

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