1. Symbols and Geometric Elements
Segment or A B
Ray A B
Line or F E

2. Ray Notation A B C D
Notice the position of the end point and the ray above.

3. Line Variations A B C D E or
Any two letters can be used to name the line.
Therefore, there can be multiple correct answers
and confusion.

4. More Symbols Mathematical Shorthand
Length or Measurement
Or Distance
A Number NOT a set of points
Segments
Set of Points

5. Inches, centimeters, feet, meters, etc.
Measurements
Just use a ruler. Measurements are arbitrary because the units of measurements are arbitrary.
Inches, centimeters, feet, meters, etc.
If a coordinate system is used on a line, then ALGEBRA comes into play.

6. Measure the Lines Below

7. Tolerance Measurements are never exact.
They are always open to interpretation.
Answers are sometimes rounded up.
Answers are sometimes rounded down.
Some visual interpretations are different. There may be a scale.
The degree of accuracy depends on the accuracy of the equipment.
The degree of accuracy depends on the accuracy of measurer.

8. Coordinate Systems
Points are letters
Coordinate are numbers.

9. E
The name of the red pt. is ___ The coordinate of the red pt. is ___ The name of the grey pt. is ___ The coordinate of the grey pt. is __ J 5

10. Find the coordinates
J = ___
A = ___
C = ___
K = ___ 5 -4 -2 6

11. Calculation of Distance Using Coordinates5 3
You could simply count the blocks.
The answer is 2.

12. Calculation of Distance Using Coordinates33 3
Counting blocks would be time consuming.
You could simply subtract.
Subtraction means the difference between numbers.
The answer is 30.

13. Calculation of Distance Using Coordinates-8 33
You could simply subtract.
33 – (-8) = = 41
Note that negative numbers requires using algebra.
The answer is 41.

14. You could simply subtract.-8 -5
You could simply subtract.
-5 – (-8) = = 3
However if we subtract the numbers in reverse, then...
-8 – (-5) = =
- 3
Therefore to avoid negative numbers,
we take the absolute value of the differences.

15. Distance = a b You subtract the coordinates
then take the absolute value
of the difference.
Distance =

16. 1 1 1 3 4 4 5 9 Method 1: Count the blocks.
Method 2: Subtract coordinates and
take the absolute value. 1 5 9 1

17. 1 1 2 2 3 4 4 5 9 Method 1: Count the blocks.
Method 2: Subtract coordinates and
take the absolute value. 1 5 9 2

18. 1 3 1 3 2 3 4 4 5 9 Method 1: Count the blocks.
Method 2: Subtract coordinates and
take the absolute value. 1 5 9 3

19. 1 3 1 2 3 5 9 3 Method 1: Count the blocks.
Method 2: Subtract coordinates and
take the absolute value. 3

20. 1 3 1 2 3 4 5 9 4 Method 1: Count the blocks.
Method 2: Subtract coordinates and
take the absolute value. 4

21. 1 3 1 2 3 4 4 5 9 4 Method 1: Count the blocks.
Method 2: Subtract coordinates and
take the absolute value. 4

22. 1 3 1 2 3 4 4 5 5 Method 1: Count the blocks.
Method 2: Subtract coordinates and
take the absolute value. 3 4 4 1 5 5

23. 1 3 1 2 3 4 4 5 9 9 Method 1: Count the blocks.
Method 2: Subtract coordinates and
take the absolute value. 3 4 4 1 5 9 9

24. Ruler Postulate
The points on a line can be paired up with real numbers in such a way that any two points can have coordinates of 0 or 1.
Once the coordinates have been chosen in this way, the distance between the any two points is the absolute value of the difference of their coordinates.
The measuring scale is arbitrary.

25. If M is on the segment and
M is a midpoint of
If M is on the segment and
It is necessary for both conditions. Let’s see why?

26. The midpoint Must be on the Segment! D, E, and F
Are equidistant from both A and B
But they are NOT midpoints.
The midpoint
Must be on the
Segment!

27. Bisectors
Bisectors can be any segment, ray, line, or plane if they go thru the midpoint of a segment.

28. D is midpoint of E is midpoint of C is midpoint of B is midpoint of
Find the value of their coordinates.

29. 8 4 8 12 2

30. Symbol Scramble Line Ray Segment length of Length of Measure of

31. NO Congruent Figures Yes Same Size and Shape Not the same shape
Not the same size
Not the same size NO
Yes

33. Distance Between Coordinates
12 8

34. Sometime, Always & Never
The length of a segment is ______ negative.
If point S is between points A and B, then S _____ lies on the segment.
A coordinate can ______ be paired with a point on a number line.
A bisector of a segment is __________ a line.
A ray ______ has a midpoint.
Always
Always
Sometimes
Never

35. Sometime, Always & Never
A ray _____ has an endpoint.
Congruent segments ______ have equal lengths.
and _____ denote the same rays.
A line _____ has one midpoint.
A ____ has many midpoints. Why?
Always
Always
Never
Never
Always

36. Segment Addition PostulateB C
If B is between A and C, then….
AB + BC = AC
Note:
Between means that A, B, and C are collinear.
B must be on the segment AC.

37. Segment Addition Postulate Applications
AB = 8
BC = 22
AC = ? A B C 22 8 x
= x
First, label the diagram.
30 = x
Second, find equation.
Third, solve equation.

38. Segment Addition Postulate ApplicationsB
AB = 8
AC = 22
BC = ? A C 8 x 22
8 + x = 22
First, label the diagram.
Second, find equation.
x = 14
Third, solve equation.

39. Segment Addition Postulate ApplicationsB C
AB = 3x - 4
BC = 2x + 7
AC = 18
Find AB & BC
3x - 4
2x + 7 18
3x x + 7 = 18
First, label the diagram.
5x + 3 = 18
Second, find equation.
5x = 15
Third, solve equation.
x = 3
Not done yet?

40. Segment Addition Postulate ApplicationsB C
AB = 3x - 4
BC = 2x + 7
AC = 18
Find AB & BC
3x - 4
2x + 7 18 5 13
Substitute Back in.
3x x + 7 = 18
3x - 4
2x + 7
5x + 3 = 18
3(3) - 4
2(3) + 7
5x = 15
6 + 7 = 13
9- 4 = 5
x = 3

41. Segment Addition Postulate Applications
AB = 3x - 13
BC = 16
AC = 4x + 14
Find AB & AC A B C
3x - 13 16
4x - 4
Label diagram.
3x = 4x - 4
Find equation.
3x+3 = 4x - 4
Not Done Yet
NDY
- x = - 7
Solve equation.
x = 7

42. Segment Addition Postulate Applications
AB = 3x - 13
BC = 16
AC = 4x + 14
Find AB & AC A B C
3x - 13 16
4x - 4 8 24
Substitute into expressions.
3x = 4x - 4
3x - 13
4x - 14
3x+3 = 4x - 4
3(7) - 13
4(7) - 14
- x = - 7 8 24
x = 7

43. You must be able to do these
complex algebraic problems.
They will be in the chapter test and
the marking period exam (QPA)

44. Summary A B C D F E B C There are several symbols for geometric terms.
No symbol means…
The distance from B to C.
A numerical value. B C

45. Summary 2 5 5 There are alternate symbols for
distance, length, or measurement. A B
Measurements are always arbitrary due to
the choice of units (meters, feet, etc.),
degree of accuracy and
scale. 5 5

46. Summary 3 The letters are the names of the points.
The numbers are the coordinates that indicate
the relative position of each point.

47. Summary 4 The ruler postulate allows us to…
1. Build number lines at any scale.
2. Compute distance by taking
the absolute value of the
difference of the coordinates.

48. Summary 5 The distance on a line is the sum of its parts. AB + BC = AC
The segment addition postulate
allows us to conclude…
The distance on a line is
the sum of its parts. A B C
AB + BC = AC

49. Summary 6 A B C AB = 3x - 4 BC = 2x + 7 AC = 18 Find AB & BC 3x - 4
You must be able to do these algebraic problems.

50. C’est fini.
Good day and good luck.