1.1.1B Measuring Segments
Transcript of 1.1.1B Measuring Segments
Measuring Segments
Objectives:
• Calculate the distance between two points
• Set up and solve linear equations using segment addition and midpoint properties
• Correctly use notation for distance and segments
• distance The absolute value of the difference of the coordinates. Also called the length.
Example:
The distance from R to S is written RS
Distance is alwaysalwaysalwaysalways positive. If you come up with a negative answer, you’ve done something wrong!
Notation: Notice the different notations:
AB line AB
segment AB
AB length AB
R S
AB
= − − = − =RS 2 3 5 5
congruent segments
Segments that have the same length.
Notation: “Tick marks” indicate congruent segments.
YX
A B
Since XY AB, XY AB= ≅
• •
t
between Point B is between two points A and C if all three points are collinearcollinearcollinearcollinear and
AB + BC = AC.
(part + part = whole)
Note: This is also called the Segment Segment Segment Segment Addition PostulateAddition PostulateAddition PostulateAddition Postulate.
●
A B C
bisect
midpoint
To cut or divide into two congruent pieces.
Example:
Point B bisects bisects bisects bisects FI ⇒ FB = BI
The point that bisects a segment.
Example: Point B is the midpointmidpointmidpointmidpoint of
●
F B I
FI
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 + 7 and EA = 5x — 2. Find SA.
DG
SY
SA
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D O G
16
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S K Y
24
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S E A
2x+7 5x—2
DO + OG = DG16 + 16 = 32
SK = ½ SY = ½(24) = 12
SE = EA2x + 7 = 5x — 2
9 = 3xx = 3
SA = SE + EA= 2(3)+7+5(3)-2= 26
construction A method of geometric drawing that uses only a compass and a straightedge.
Constructing a figure is different from just sketching it. Construction has been used in Geometry since ancient times, in both philosophical and practical ways.
In class, you will learn to construct
• congruent segments
• segment midpoints
• segment bisectors