1. Session 55
Draw six segments that pass through every dot in the figure without taking your pencil off the paper.

2. Go over test
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

3. Unit 5 Vocabulary
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

4. Angle
Two rays with a common endpoint called the vertex
The angle is

5. Circle
The set of points on a plane at a certain distance, or radius, from a single point, the center

6. Perpendicular Line Two lines that intersect at a right angle (90°).
Written as

7. Parallel Line
Lines in a plane that either do not share any points and never intersect, or share all points.
Written as

8. Line Segment
A line with two endpoints.
Written as

9. Point An exact position or location in a given plane.
Point A or Point B

10. Line
The set of points between points P and Q in a plane and the infinite number of points that continue beyond the points.
Written as

11. Distance along a line
The linear distance between two points on a given line.

12. Right Angle
An angle that measures 90°.

13. Acute Angle
An angle measuring less than 90° but greater than 0°.

14. Obtuse Angle
An angle measuring greater than 90° but less than 180°.

15. One-to-One
A relationship wherein each point in a set of points is mapped to exactly one other point.

16. Pre-image
The original figure before undergoing a transformation.

17. Image
The new, resulting figure after a transformation

18. Isometry
A transformation in which the preimage and image are congruent.

19. Every segment is congruent to its image.
Transformations are called RIGID if every image is congruent to its preimage.
Rigid transformations can also be referred to as an ISOMETRY.
Every segment is congruent to its image.

20. Which of the following are rigid transformations? (Isometry)

21. Isometries not only preserve lengths, but they preserve angle measures parallel lines, and betweenness of points

22. Find the value of each variable, given that the transformation is an isometry.

23. Congruent
Figures are congruent if they have the same shape, size, lines, and angles.

24. Similar Triangles
Triangles are similar if they have the same shape but have different sizes.

25. Even and Odd Functions
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

26. Algebraically A function is even if A function is odd if
All of the exponents of the variable are even.
A function is odd if
All of the exponents of the variable are odd.
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.
A function is neither if
The exponents are a mixture of odd and even

27. All constants really have a x0
BEWARE OF CONSTANTS
All constants really have a x0
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

28. x0 is EVEN!!
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

29. Graphically A function is even if A function is odd if
The graph reflects across the y-axis
(means you can fold it hotdog style and it would match up).
A function is odd if
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.
The graph has 180 rotational symmetry about the ORIGIN
(means you could turn it upside-down & it would still look the same...it must go through the origin).

30. Even, Odd or Neither?
Ex. 1
Algebraically 1
ODD

31. Even, Odd or Neither?
Ex. 2
Algebraically x0
EVEN

32. Even, Odd or Neither?
Ex. 3
Graphically
EVEN

33. Even, Odd or Neither?
Ex. 4
Graphically
Neither 

34. Even, Odd or Neither? 1 x0
EVEN
ODD

35. Even, Odd or Neither? x0
ODD
ODD
Even

36. Even, Odd or Neither? 1
1 x0
neither
ODD
neither

37. Even, Odd or Neither? 
EVEN
ODD

38. Even, Odd or Neither?  
EVEN
Neither
ODD

39. If the dots shown are part of an even function, what points are also on the function?

40. If the dots shown are part of an odd function, what points are also on the function?

41. HW Practice WS