Section 1-3 Segments, Rays, and Distance. line; segment; ray;
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Transcript of Section 1-3 Segments, Rays, and Distance. line; segment; ray;
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Section 1-3
Segments, Rays, and Distance
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line; 𝐴𝐵 ,𝐵𝐴
segment;𝐴𝐵 ,𝐵𝐴
ray;
ray; ,
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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
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common endpointopposite
,
,
,
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Postulates: ________________________________
Theorems: _________________________________
__________________________________________
a statement accepted without proof
a statement proved with a postulate
and/or definition.
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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.
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|−2−0||0−3||3−5||−2−3||0−5|
2
3
2
5
5
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|−10−30||−40|
40
|5−25||−20|
20
|−30−(−5)||−25|
25
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Segment Addition Postulate: If B is between A & C, then AB + BC = _____.AC
little segment + little segment = big segment
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AB + BC = AC4 + 8 = AC
12 = AC
12
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AB + BC = AC(2x) + (x + 7) = 16
3x + 7 = 163x = 9
x = 3
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AB + BC = AC(3x) + (4x + 2) = 30
7x + 2 = 307x = 28
x = 4
BC = 4x + 2BC = 4(4) + 2BC = 16 + 2BC = 18
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size shape
congruence symbol
equal lengths
•
• •
•
E
D
F
GIf =, then know
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divides 2
(=)
Y is the midpoint of or
XY = YZ
* Know the length
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AB + BC = AC(4x) + (4x) = 32
8x = 32x = 4
4x 4x32
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(3x + 2) = (4x + 1)1 = xx = 1
AB = 3x + 2AB = 3(1) + 2AB = 3 + 2AB = 5
5 5
AC = 10
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linesegment rayplane
midpoint
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HOMEWORK:page 15 #2-26 even