1. Segments, Rays, and Distance
Geometry 1-3
Segments, Rays, and Distance

2. Review: The Point The point is an exact location
Like an infinitely small dot
Named with a capital letter Q
Point Q

3. Review: The Line If we string an infinite number of points
straight out in both directions…
A one-dimensional line is formed
Named with a lower case letter or two points on the line U C
Going on forever
Going on forever
UC or CU

4. Review: The Plane If we string and infinite number of lines
in both directions…
Named with three or more
points in the plane
A two-dimensional plane is formed.

5. The Ray Chop! If we string an infinite number of points
straight out in only one direction…
A one-dimensional ray is formed
Chop!
Named with the endpoint and another point on the ray GZ G Z
It is like a line that has been chopped at one end.
Going on forever

6. The Ray
Ray – a piece of a line that has one endpoint and continues infinitely in only one direction
Opposite rays – two rays with a common endpoint that extend in opposite directions (making a line)

7. The Segment Double Chop!
If we draw an infinite number of points between
2 endpoints, it gives us a piece of a line of
finite length…
NO or ON
Double
Chop!
A line segment is formed. N O
It is like a line that has been chopped at both ends.

8. The Segment Segment -- a piece of a line with a specific length A B AB
“segment AB”

9. Length
length of a line segment – length of a segment is defined as the distance between the endpoints of the segment
--the length of AB (previous) would be denoted as AB

10. Notebook Terms
Postulate or Axiom – a statement that is accepted as true
Theorem – a statement that can be proven

11. Ruler Postulate
Ruler Postulate – any line can be made into a number line such that the distance between any two points is the absolute value of the difference of their coordinates.

12. Segment Addition If B is between A and C then, AB + BC = AC A B C 53 Z
x + 12 I
2x – 7 P

13. Congruent
Same size, same shape
Congruent segments have equal lengths

14. Midpoints and Bisectors
The midpoint of a segment is in the exact middle
A bisector is anything that passes through the midpoint