1. DRILL
If A is in between points B and C and AC is 4x + 12 and AB is x – 4 and BC is 57 feet how long is AB?
Angles A and B are Supplementary if Angle A is 2x – 20 and Angle B is 4x – 44. Find the measure of Angle A.

2.                                                                                                                                                                                                                                                                           
Transformations
A transformation is any type of movement in geometry, it can be a change in shape, size, or simply location of an object.
The three types of Transformations we will talk about today are Reflections, Rotations and Translations.

3. Pre-Image And Image
Pre-Image is the original figure before any type of transformation takes place.
Image is the new figure after the transformation has taken place.

4. DO YOU SEE MATH IN THIS PICTURE?

5. What about this one?

6. How about now?

10. Vocabulary
Isometry: a transformation in which the original figure and it’s image are congruent.
Opposite Orientation: when an image appears to be backwards compared to the pre-image.

11. Reflection
A transformation in which a line of reflection acts as a mirror reflecting points from their pre-image to their image.

13. Reflections A reflection reverses orientation.
A reflection is an isometry.
A reflection over the x-axis results in a change in the y-coordinate.
A reflection in the y-axis results in a change in the x-coordinate.

14. Symmetry Objective: Today, we will identify types of
symmetry in figures.

15. Reflectional Symmetry/Line Symmetry
A figure has reflectional symmetry if and only if a line coincides with the original figure.
The line is called the axis of symmetry.

16. Reflectional Line of Symmetry
A figure has reflectional symmetry if and only if there exists a line that “cuts” the figure into two congruent parts, that fall on top of each other when folded over the line of symmetry.

17. Examples
Name all the types of symmetry each figure has: (if rotational state how many degrees)
Rotational Symmetry (180)
Or Point Symmetry
Reflectional Symmetry (1)
Reflectional Symmetry (8)
Rotational Symmetry (45)

18. Alphabet Language Horizontal Line Vertical Line Rotational Symmetry
ENGLISH
(Uppercase)
GREEK

19. Greek Alphabet

20. ENGLISH GREEK Language Horizontal Line Vertical Line Rotational
Symmetry
ENGLISH
GREEK

21. Which category does it fit?

22. Which category does it fit?

23. Which category does it fit?

24. Reflection
Fold patty paper both ways, so that you have 4 boxes. Darken the folds and label the x and y axes.
Draw any TRIANGLE in the 2nd Quadrant

25. Reflection Reflect your triangle over the x-axis.
What are the new coordinates?

26. Reflection Reflect your original triangle over the y-axis
What are the new coordinates?

27. Reflection Reflect your original over the line y = x.
What are the new coordinates?

28. Rotations

29. Rotation
A rigid motion that moves a geometric figure about a point known as the turn center.

30. Properties of a Rotation
A rotation is an Isometry.
A rotation does not change orientation.

31. Finding The Angle Of Rotation
Find the number of congruent images under a rotation and then divide that number into 360.
EX:

32. Rotation of 180 Degrees
A Rotation of 180 Degrees is equivalent to a reflection over the origin.
(x, y) becomes (-x, -y)

33. Rotational Symmetry
A figure has rotational symmetry of “n” degrees if you can rotate the figure “n” degrees and get the exact same image.
N must be between 0 and 360.

34. Rotational Symmetry
Wind Mill
How many degrees can each rotate?