1-5 Measuring Segments

1
1-5 Measuring Segments

• Find the distance between two points using the
  Ruler Postulate
• Determine the length of a segment using the
  Segment Addition Postulate

2
Finding Segment Lengths

• Simulation for measuring segments or hands-on
  measuring activity with broken ruler
• http//www.geogebra.org/en/upload/files/english/du
  ane_habecker/broken_cm_ruler.html

3
Ruler Postulate

• Given two points, the two points can be paired
  one to one with two real numbers.
• The real numbers are called the coordinates of
  the points
• To find the distance between the two points,
  subtract the coordinates then take the absolute
  value (to ensure a positive distance)

4
Example 1

• Find DE (distance between D and E)

DE 0 (2) -2 2
5
Example 2

• Find AB (distance between A and B)

AB -8 (-5) -3 3
6
Example 3

• Find BC (distance between B and C)

BC -5 (-2) -3 3
7
Example 4
AB -8 (-5) -3 3 BC -5 (-2)
-3 3
8
Segment Addition Postulate
A
B
C

• If three points A, B, and C are collinear and B
  is between A and C,
• then AB BC AC

9
Example 1
Find ST.
QS 8
QT 12
QS ST QT
ST QT QS
ST 12 8 4
10
Example 2
ST 3x 12
DS 2x 8
DT 60. Find x, 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

11
Midpoint of a Segment
A
B
C

• A midpoint of a segment divides the segment into
  two congruent segments.
• The two marks indicate that the two segments are
  congruent.
• AB ? BC

12
Using the Midpoint
2x 1
3x 4
B
A
C
Given C is the midpoint of AB. Find AC, CB,
and AB.

• 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

13
Learning Check and Summary

• Suppose X, Y, and Z are collinear. If XY 10
  and XZ 6 and YZ 4, which point lies between
  the other two points?
• The midpoint of a segments splits the segment
  into two ___?___ segments

14
Homework

• Workbook 1-5 pp. 257-258