Ch 1‐3: Definitions, Lines, and Line Segments
Definition‐ a statement of the precise meaning
of a term
Qualities of a GOOD definition:
‐ express is words that have already been defined
or excepted as undefined words
‐ must be reversible
‐ must state the class the word belongs to
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Collinear Points
DEFINITION: Collinear Set of Points‐ a set of points that all lie on the same straight line
DEFINITION: Noncollinear Set of Points‐ a set of 3 or more point that do NOT lie on the same straight line
The DISTANCE between 2 points‐ find the difference between the 2 coordinates assigned to these points on a number line
A B C D E F G
Absolute Value‐ the difference between 2 coordinates is a positive value
ex) l 1 ‐ 5 l = l‐4l = 4 DEFINTION: Distance between any 2 points on the real number line‐ is the absolute value of the difference of the coordinates of the 2 points
AB = la‐bl OR BA = lb‐al
Betweenness of points on a line‐ 3<4<6 then 4 is between 3 and 6
DEFINTION: B is BETWEEN A and C‐ IFF A,B and C are distinct collinear points and AB + BC = AC
To name: 3 Capital letters to represent 3 points
EX) ABC ; where B is between A and C
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Line Segment
DEFINTION: Line segment, or segment‐ a set of points consisting of 2 points on a line, called endpoints, and all points on the line between the endpoints
DEFINTION: Length or Measure of a line segment‐ find the distance between the endpoints
*** AB represents line AB
*** AB represents segment AB
*** AB represents the measure of length of AB
DEFINITION: Congruent Segments‐ segments that have the same measure
A
B AB ≅ CD segment AB is congruent to segment CD
C
D AB = CD the measures or distances are the same
***You may use either notation
DEFINITION: Midpoint of a line segment‐ point of the line segment that divides the segment into 2 congruent segments
If M is the midpoint of AB, then AM≅MB or AM = MB
AM= 1/2AB, MB= 1/2AB, AB=2AM, AB=2MB
DEFINITION: Bisector of a line segment‐ any line or subset of a line that intersects the segment at its midpoint
DEFINTION: A line segment RS is the Sum of 2 lines segments RP and PS if point P is between points R and S. ***RS = RP + PS
***RP = RS ‐ PS
***PS = RS ‐ RP
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HOMEWORK: PAGE 11
#1­6, 7­13, 19­22, 34­36, 39­42, 43­46,52,58,59
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