1. 1.7 Motion in Geometry

2. Rigid Transformations
Transformations that do not change shape or size.
Preimage is the original shape
Image is the shape that undergoes a transformation
preimage
image

3. NOTATION We’ll call this shape ABCDEFG
Many times the vertices are labeled.
We’ll call this shape ABCDEFG
NOTATION A G F E D C B
This is the PREIMAGE A’ G’ F’ E’ D’ C’ B’
When the pre-image is transformed, (rotated, translated, or reflected) it becomes:
A’B’C’D’E’F’G’
The image of each vertex has a small tick mark. We say ‘prime’ every time we see one of them.
This notation allows us to know which is the image and which is the pre-image – which, since they are rigid – are 2 identical figures.
This is the IMAGE

4. A little extra, free informationH H’
If we started with pre-image H and it was transformed, then the image would be H’.

5. Hang in there M C L B P N A O E D
ABCDE LMNOP

6. Transformations There are 3 types of rigid transformations:
Translation – shapes slide along a straight path
Rotation – shapes turn about a point
Reflection – shapes flip across a line
Hello.
Hello.

7. Translation Shapes slide
Every point of a figure moves in a straight line, all points move the same distance and same direction.

8. Rotation Rotations turn
Every point of a figure moves around a given point called the center of rotation.

9. Reflection Glide Reflection Reflections flip.
In a reflection, a line plays the role of a mirror. Every point in a figure is ‘flipped’ across the line.
Glide Reflection

10. Glide Reflection
This refers to a shape that is translated and reflected… like footprints on a beach.

11. Summary What is the movement of a rotation?
What does is ‘turn’ around?
What is the movement of a translation?
What does it ‘slide’ on?
What is the movement of a reflection?
What does it ‘flip’ over?
When can the pre-image and the image be a different size?
How do you notate the pre-image? (For instance segment AB)
How do you notate the image?

12. Summary… part 2
If I referred to the image M’, would that be the image or preimage?
Give an example of a rotation.
Give an example of a translation.
Give an example of a reflection.
Give an example of a glide reflection.
What is the conditional of ‘my mom is beautiful’?
What is the truth value?
What is the converse of ‘my mom is beautiful’?
Are you able to write a biconditional?

13. Game of War Get a partner, a pencil and one piece of paper.
Fold the paper hamburger
With a straight edge, trace the fold
On your side, put 5 war things no bigger than a dime. Don’t group them together, spread them out.
Try and hit the other person’s items by drawing a bomb on your side, folding the paper and tracing the bomb.

14. BONUS!!!! I’m looking for two things…..
Tell me the relationship between the pre-image of the bomb and the image of the bomb with the fold line.
Tell me the relationship between a segment drawn between the pre-image and image of a bomb with the fold line.

15. Assignment
Motion in Geometry
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