RULER POSTULATES

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RULER POSTULATES SEGMENT ADDITION
This stuff is AWESOME!
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POSTULATE

• A STATEMENT ABOUT GEOMETRIC FIGURES ACCEPTED AS
  TRUE WITHOUT PROOF.

3
Ruler Postulate

• The points on a line can be placed in a
  one-to-one correspondence with real numbers so
  that
• For every point on the line, there is exactly one
  real number.
• For every real number, there is exactly one point
  on the line.
• The distance between any two points is the
  absolute value of the difference of the
  corresponding real numbers.

4
Ruler Placement Postulate

• Given two points, A and B on a line, the number
  line can be chosen so that A is at zero and B is
  at a positive number.

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NOTATION
AB means the line segment with endpoints A and
B. AB means the distance between A and B.
A
B
AB 14 cm
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BETWEEN
D
E
G
E is between C and D. G is not between C and
D. For one point to be between two other points,
the three points must be collinear.
C
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SEGMENT ADDITION POSTULATE
If Q is between P and R, then PQ QR PR.
What does this mean?
Start with a picture
P
R
Q
If point Q is between points P and R, then the
distance between P and Q plus the distance
between Q and R is equal to the distance between
P and R.
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SEGMENT ADDITION POSTULATE
If PQ QR PR, then Q is between P and R.
What does this mean?
If the measure of segment PQ plus the measure of
segment QR is equal to the measure of segment
PR, then point Q must be between points P and R.
12
3
PR 15
P
R
Q
14
3
Q
15
P
R
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NOTE CARD

• Segment Addition Postulate 2
• If Q is between P and R, then PQ QR PR.
• If PQ QR PR, then Q is between P and R.

P
R
Q
10
N is between L and P. LN 14 and PN 12.
Find LP.
14
12
L
P
N
Q is between R and T. RT 18 and QR 10. Find
QT.
10
R
T
Q
18
11
Find MN if N is between M and P, MN 3x 2, NP
18, and MP 5x.
3x 2
18
M
P
N
5x
MN 3 (10 ) 2 MN 32
3x 2 18 5x 3x 20 5x -3x
-3x 20 2x 2
2 10 x