Download Slide 1 - Katy Tutor

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
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p. 31 TxtBk: Finding Segment Lengths
• Simulation for measuring segments or
hands-on measuring activity with “broken”
ruler
•
http://www.geogebra.org/en/upload/files/english/duane_habecker/broken_cm_ruler.html
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)
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P. 32 TxtBk Ex. 1
A
-8
B
-7
-6
-5
C
-4
-3 -2
D
-1
0
E
1
2
• Find DE (distance between D and E)
• Find AB (distance between A and B)
AB = | -8 – (-5) | = | -3 | = 3
Find BC
BC = | -5 – (-2) | = | -3 | = 3
So AB = BC and
AB ≅ BC (Congruence of segments)
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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
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Example: Segment Addition Postulate
P
Q
S
QS = 8
Find ST.
T
QT = 12
QS + ST = QT
ST = QT – QS
ST = 12 – 8 = 4
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p. 32 TxtBk Ex. 2
D
DS = 2x – 8
S ST = 3x – 12
T
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
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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
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Using the Midpoint
3x – 4
2x + 1
A
C
B
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
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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
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