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# Geometry - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Geometry' - barclay-cain

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Presentation Transcript

### Geometry

Lesson 4 – 7

Congruence Transformations

Objective:

Identify reflections, translations, and rotations.

Verify congruence after a congruence transformation.

• Transformations –

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

• AKA rigid transformations

• AKA isometric (isometry)

• The position of the image may differ from that of the preimage, but the two figures remain congruent.

• Reflection

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

• Translation

• A transformation that moves all points of the original figure the same distance in the same direction. A slide of the points

• 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.

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

Rotation

Reflection

Translation

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

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

Translation

Reflection

Verify Congruence after Transformation diagram as a reflection, translation, or rotation.

• 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 diagram as a reflection, translation, or rotation.

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

Homework diagram as a reflection, translation, or rotation.

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