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2-2: SEGMENTS AND PROPERTIES OF REAL NUMBERS
2-2: Segments & Properties of Real Numbers
BETWEENNESS: A point is between two points if and only if all three points are collinear, and the two points are on opposite sides of the third point.
Point K is between points A and L, because A, K & L are all on the same line and AK + KL = AL
Point B is not between points A and D, because B is not on the same line as A & D
A
B
K
M
S
L D
2-2: Segments & Properties of Real Numbers
Example Points A, B, and C are collinear. If AB = 12,
BC = 47, and AC = 35, determine which point is between the other two. Check to see which two measures add to equal
the third. 12 + 35 = 47 AB + AC = BC Therefore, point A is between points B and C
Points R, S and T are collinear. If RS = 42, ST = 17, and RT = 25, determine which point is between the other two. Point T
2-2: Segments & Properties of Real Numbers
Some properties of real numbers (Copy only if necessary) Reflexive Property
For any number a, a = a Symmetric Property
For any numbers a and b, if a = b, then b = a Transitive Property
For any numbers a, b and c, if a = b and b = c, then a = c
Addition and Subtraction Properties For any numbers a, b, and c, if a = b, then:
a + c = b + c and a – c = b – c Multiplication and Division Properties
For any numbers a, b, and c, if a = b, thena c = b c, and (if c ≠ 0), a/c = b/c
Substitution Property For any numbers a and b, if a = b, then a may be
replaced by b in any equation
2-2: Segments & Properties of Real Numbers
EQUATION: A statement that includes the symbol = Example: If QS = 29 and QT = 52, find ST
QS + ST = QT Definition of Betweenness 29 + ST = 52 Substitution Property 29 + ST – 29 = 52 – 29 Subtraction Property ST = 23 Substitution Property
Using the line above. If PR = 27 and PT = 73, find RT.
P Q R S T
46
2-2: Segments & Properties of Real Numbers
Measurements are composed of two parts: the measure and the unit of measure. The measurement of a segment is also called the length of a segment.
Example in class of using a ruler PRECISION: depends on the smallest unit of
measure being used. GREATEST POSSIBLE ERROR: half the
smallest unit used to make the measurement. PERCENT OF ERROR:
greatest possible errorpercent of error = x 100%
measurement
2-2: Segments & Properties of Real Numbers
Percent Error example using cm Measurement 5.7 cm (57 mm) Precision: 1 mm Greatest Possible Error: 0.5 mm Percent of Error:
Percent Error example using in Measurement: 2 ¼ in (2.25 in) Precision: 1/16 in (0.03125 in) Greatest Possible Error: 1/32 in Percent of Error:
.5100% .88%
57
.03125100% 1.39%
2.25
2-2: Segments & Properties of Real Numbers
Assignment Worksheet #2-2 Additionally, for problems 11-14, calculate
the percent error (both in and cm)