1. 4-7 Congruence Transformations
You proved whether two triangles were congruent.
Identify reflections, translations, and rotations.
Verify congruence after a congruence transformation.

2. Transformation
A second figure that looks exactly like the first but is shifted, flipped, rotated or changed the size.
A transformation is an operation that maps an original geometric figure, the pre-image, onto a new figure called the image.

3. What happened?
Flip
Moved
Rotated

4. tells you that A is mapped to X, B is mapped to Y, and C is mapped to Z. Y B
image X Z
Preimage
(Original figure) A C

5. Pre-Image/Image Pre-image the original figure
Image the figure after a transformation A B B′ A′ C C′ l
Pre-image (1)
Image (2)

6. Pre-image/Image To tell the two images apart, use prime notation A′.
When naming images of figures, list corresponding points in the same order.

7. A congruence transformation, also called a rigid transformation or an isometry, is one in which the position of the image may differ from that of the preimage, but the two figures remain congruent.
The three main types of congruence transformations are:
Reflection
Translation
Rotation

8. Page 296

9. Name the three main types of congruence transformations…
Reflections
Rotations
Translations

10. A. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are in the same position, just 5 units right and 2 units down.
Answer: This is a translation.

11. B. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are the same distance from the origin. The angles formed by each pair of corresponding points and the origin are congruent.
Answer: This is a rotation.

12. C. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are the same distance from the x-axis.
Answer: This is a reflection.

13. A. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these

14. B. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these

15. C. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these

16. 4-7 Assignment
Page 299, 7-16, 24-27