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2-2: Segments and Properties of Real Numbers

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.

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2-2: Segments and Properties of Real Numbers

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  1. 2-2: Segments and Properties of Real Numbers

  2. 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 S K D M L B A

  3. 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

  4. 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

  5. 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 – 29Subtraction Property • ST = 23 Substitution Property • Using the line above. If PR = 27 and PT = 73, find RT. T Q R S 46 P

  6. 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:

  7. 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:

  8. 2-2: Segments & Properties of Real Numbers • Assignment • Worksheet #2-2 • Additionally, for problems 11-14, calculate the percent error (both in and cm)

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