Download Segment Addition Postulate

Pre-AP Geometry
Measuring Segments
Name_________________________________________
Period______
Ruler Postulate
P
Points on a line can be paired with real numbers so
that the distance between any
two numbers is the absolute value of the difference.
Q
*DISTANCE IS ALWAYS POSITIVE!!!*
IMPORTANT:
The length of
PQ  PQ  p  q
is the absolute value of the difference.
Example 1: Find RS, ST, and RT:
R
-4 -3
S
-2
-1 0
T
1
2
3 4
1. RS 
Important:
2. ST 
 No signs above letters means
to find distance or length.
3.. RT 
The measures found above show a relationship: one point is BETWEEN two others.
BETWEEN: can only be applied to collinear points
Example 2: T is BETWEEN pt. S and E .
E
T
L is NOT between S and T .
L
S
Segment Addition Postulate
R
Q
P
If Q is between P and R, then PQ + QR = PR.
If PQ + QR = PR, then Q is between P and R.
Practice: Find the missing values. ALWAYS USE A DIAGRAM TO ASSIST.
1. If RS  5 , and RT  12 , find ST .
R
S
2. If RS  2x and ST  5 and RT  31,
find RS .
T
3. If RS  3x  2 , ST  18 , and RT  5x ,
determine RS .
R
S
T
R
4.
S
T
If RS  6x  5 , ST  2x  3 , and
RT  30 , find RS and ST .
R
S
5. EF  4x  20 and FG  2x  30 . EG  100 . Point F is between E and G.
Find the value of x . Then find EF and FG .
First step: Draw a diagram to assist.
T
Key Terms:
1. ____________ __________- segments with equal length
Symbol:
hash marks
The same number of hash marks show congruent segments
(as shown to the right).
2. ______________ - the point that divides a segment into 2 congruent parts.
Q
PM  MQ
M
P
3. ____________ _____________ - a segment, line, or plane that intersects a segment
through its midpoint
S
QM  MR
ST bisects QR
Q
M
R
T
Example 3: Point U is the midpoint of XY . If XY  16x  6 and UY  4x  9 , find the value of x and the
measure of XY .
1. Label Diagram:
2. Solve for x (algebra):
3. Measure of XY (plug in):
Y
U
X
Example 4: Line t is a segment bisector of XY at point M, find XM and MY if XM  3x  6
MY  2x  14 .
1. Label Diagram:
2. Solve for x (algebra):
t
M
X
Y
and
3. Measure of XM and MY :
Finding a Midpoint on a Number Line:
The coordinate of the midpoint is the ______________ of the coordinates of the endpoints
The midpoint between a and b is:
ab
2
Example 5: On a number line:
-8 -7 -6 -5 -4 -3 -2 -1 0
1 2
3 4
5 6
7
8
Find the midpoint between the following coordinates:
a.
2 and 8
b.
-4 and 2
c.
1 and 6
d.
-8 and 7
Example 6: If AD  12 and AC  4 y  36 , find the value of y . Then find AC and DC .
A
B
D
E
Example 7: M is between C and W , CM  x 2 , MW  11x , and CW  60 . Find x .
C