Transcript segment addition 1.15

RULER POSTULATES &
SEGMENT ADDITION
This stuff is
AWESOME!
POSTULATE
• A STATEMENT ABOUT GEOMETRIC
FIGURES ACCEPTED AS TRUE
WITHOUT PROOF.
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.
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.
AB means the line segment with
endpoints A and B.
A
B
AB means the distance between
A and B.
AB = 14 cm
D
G
C
E
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.
If Q is between P and R, then PQ + QR = PR.
What does this mean?
Start with a picture:
P
Q
R
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.
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
P
3
PR = 15
R
Q
14
P
Q
15
3
R
NOTE CARD
Segment Addition Postulate
#2
If Q is between P and R, then PQ + QR = PR.
P
Q
R
If PQ + QR = PR, then Q is between P and R.
N is between L and P. LN = 14 and PN = 12. Find LP.
L
14
N
12
P
Q is between R and T. RT = 18 and QR = 10. Find QT.
10
R
Q
18
T
Find MN if N is between M and P, MN = 3x + 2,
NP = 18, and MP = 5x.
M
3x + 2
N
18
P
5x
3x + 2 + 18 = 5x
3x + 20 = 5x
-3x
-3x
20 = 2x
2
2
10 = x
MN = 3 (10 ) + 2
MN = 32