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

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### 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.

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

- 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

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