1. Lesson 4 – 7 Congruence Transformations
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. Rotation Reflection Translation
Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Rotation
Reflection
Translation

8. Translation Rotation Reflection
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. Translation Reflection
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 – 6 all, 8 – 28 E, 32, 38 – 42 E, 46 – 50 E