1. 1.5 Measuring
Segments
August 26, 2013

2. Today’s Objective/Goal
• By the end of the lesson, you should be able
to do the following:
Find the distance between two points using a
ruler AND applying the Ruler Postulate
Determine the length of a segment using the
Segment Addition Postulate

3. Postulate 1-5 Ruler Postulate
• The points of a line can be put into one-to-one
correspondence with the real numbers so that the
distance between any two points is the absolute
value of the difference of the corresponding
numbers.

5. Comparing Segment Lengths
• Find DE (distance between D and E)
• Find AB (distance between A and B)
-3 -1-2 10-8 2-7 -5-6 -4
D EBA C
AB = | -8 – (-5) | = | -3 | = 3
Find BC
BC = | -5 – (-2) | = | -3 | = 3
So AB = BC and
AB ≅ BC (Congruence of segments)

6. Postulate 1-6 Segment Addition Postulate
• If three points A, B, and C are collinear
and B is between A and C,
then AB + BC = AC
A
B
C

7. Segment Addition Postulate
P Q S T
Find ST.
QS + ST = QT
ST = QT – QS
ST = 12 – 8 = 4
QT = 12
QS = 8

8. Using the Segment Addition Postulate
If DT = 60, find the value of x. Then find DS and ST.
DS + ST = DT
2x – 8 + 3x – 12 = 60
5x – 20 = 60
5x = 80
x = 16
DS = 2x – 8 = 2(16) – 8 = 24
ST = 3x – 12 = 3(16) – 12 = 36
D S TST = 3x – 12DS = 2x – 8

9. Midpoint
* The two marks indicate that the two segments are
congruent.

10. Using the Midpoint
AC = CB
2x + 1 = 3x – 4
1 = x – 4
5 = x
AC = 2x + 1 = 2(5) + 1 = 11
CB = AC = 11
AB = AC + CB = 11 + 11 = 22
A C B
2x + 1 3x – 4
Given: C is the midpoint of AB. Find AC, CB, and AB.

11. Learning Check
1. Suppose X, Y, and Z are collinear. If XY =
10 and XZ = 6 and YZ = 4, which point lies
between the other two points? (Draw the
points on a line.)
2. The midpoint of a segments splits the
segment into two ___?___ segments