Section 1-3

Segments, Rays, and Distance

line; 𝐴𝐵 ,𝐵𝐴

segment;𝐴𝐵 ,𝐵𝐴

ray;

ray; ,

Ray: ______________________________________

__________________________________________

Segment: __________________________________

__________________________________________

line that has a definite starting point (called

an endpoint) that goes on forever in one direction

part of a line with definite beginning

and end. **can be measured

common endpointopposite

,

,

,

Postulates: ________________________________

Theorems: _________________________________

__________________________________________

a statement accepted without proof

a statement proved with a postulate

and/or definition.

Length of a segment:

Ruler Postulate:

- measure of a segment- named by two capital letters with no symbol on top.- always positive

- used to find the difference between two points.- take the absolute value of the difference between the coordinates.

|−2−0||0−3||3−5||−2−3||0−5|

2

3

2

5

5

|−10−30||−40|

40

|5−25||−20|

20

|−30−(−5)||−25|

25

Segment Addition Postulate: If B is between A & C, then AB + BC = _____.AC

little segment + little segment = big segment

AB + BC = AC4 + 8 = AC

12 = AC

12

AB + BC = AC(2x) + (x + 7) = 16

3x + 7 = 163x = 9

x = 3

AB + BC = AC(3x) + (4x + 2) = 30

7x + 2 = 307x = 28

x = 4

BC = 4x + 2BC = 4(4) + 2BC = 16 + 2BC = 18

size shape

congruence symbol

equal lengths

•

• •

•

E

D

F

GIf =, then know

divides 2

(=)

Y is the midpoint of or

XY = YZ

* Know the length

AB + BC = AC(4x) + (4x) = 32

8x = 32x = 4

4x 4x32

(3x + 2) = (4x + 1)1 = xx = 1

AB = 3x + 2AB = 3(1) + 2AB = 3 + 2AB = 5

5 5

AC = 10

linesegment rayplane

midpoint

HOMEWORK:page 15 #2-26 even