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Obj. 5 Measuring SegmentsObjectives:
Calculate the distance between two points on a numberline
Set up and solve linear equations using midpointproperties
Correctly use notation for distance and segments Construct
congruent segments and perpendicular
bisectors
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distance The absolute value of the difference of the
coordinates. Also called the length.
Example:
The distance from R to S is written RS
RS = | 2 3| = | 5 | = 5
Distance is alwaysalwaysalwaysalways positive. If you come
upwith a negative answer, youve donesomething wrong!
Notation: Notice the different notations:
AB line ABsegment AB
AB length AB
R S
AB
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congruentsegments
Segments that have the same length.
Notation: Tick marks indicate congruentsegments.
YX
A B
Since XY AB, XY AB=
t
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between Point B is betweentwo points A and C if all
three points are collinearcollinearcollinearcollinear andAB + BC
= AC.
(part + part = whole)
Note: This is also called the
SegmentSegmentSegmentSegmentAddition PostulateAddition
PostulateAddition PostulateAddition Postulate.
A B C
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bisect
midpoint
To cut or divide into two congruent pieces.
Example:
Point B bisectsbisectsbisectsbisects FI FB = BI
The point that bisects a segment.
Example: Point B is the midpointmidpointmidpointmidpoint of
F B I
FI
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Examples 1. O is the midpoint of and DO = 16.
Find DG.
2. K is the midpoint of and SY = 24.Find SK.
3. E is the midpoint of ; SE = 2x + 7and EA = 5x 2. Find SA.
DG
SY
SA
D O G16
S K Y
24
S E A
2x+7 5x2
DO + OG = DG16 + 16 = 32
SK = SY = (24) = 12
SE = EA2x + 7 = 5x 29 = 3x
x = 3
SA = SE + EA= 2(3)+7+5(3)-2
= 26
