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FoG - 2.1 and 2.2

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ejfischer
ejfischer

- Reviews the properties of real numbers - Appies real numbers to segments and lines - Introduces Midpoint and Distance in 1 Dimension - Introduces Segment Addition

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Foundations of Geometry 2.1 and 2.2
Real Numbers Whole numbers = counting numbers & 0 Integers = whole numbers and their negatives Rational Numbers = can be written as a fraction of integers Terminating has a finite number of digits, ends 1/8 = 0.125 Nonterminating repeat, but never end 1/7 = 0.142857142857. = 0.142857 Irrational Numbers never repeat and do not end = 3.141592654. 2 = 1.414213562.
Properties of Equality for Real Numbers Reflexive a=a Symmetric If a = b, then b = a Transitive If a = b and b=c, then a=c Addition and Subtraction If a = b, then a + c = b + c and a - c = b - c Multiplication and Division If a = b, then ac = bc and if c0 then a/c = b/c Substitution If a = b, then a may be substituted for b in any equation.
Number Lines Real numbers can be superimposed on a line to provide coordinates of points. A point is selected as the starting point, or origin. Numbers to the left or the origin are negative, to the right positive. A B C D -2 -1 0 1 2 3
Distance on a Number Line The distance between points is found by taking the positive difference in their coordinates Length (distance) A(Xa) to B (Xb) d = AB = | Xb Xa | Absolute value | a | Means to take what ever is inside and make it positive |8|=8 | -8 | = 8
Segments and Bteweenness B is between A and C if it is on the same line and to the right of one, and to the left of the other. For any B between A and C, segment addition: A B C AB + BC = AC For endpoints A and B, the Midpoint (M): M = 1/2(A + B)
References Glencoe: Geometric Concepts and Applications Section 2.1 and 2.2

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FoG - 2.1 and 2.2

  • 2. Real Numbers Whole numbers = counting numbers & 0 Integers = whole numbers and their negatives Rational Numbers = can be written as a fraction of integers Terminating has a finite number of digits, ends 1/8 = 0.125 Nonterminating repeat, but never end 1/7 = 0.142857142857. = 0.142857 Irrational Numbers never repeat and do not end = 3.141592654. 2 = 1.414213562.
  • 3. Properties of Equality for Real Numbers Reflexive a=a Symmetric If a = b, then b = a Transitive If a = b and b=c, then a=c Addition and Subtraction If a = b, then a + c = b + c and a - c = b - c Multiplication and Division If a = b, then ac = bc and if c0 then a/c = b/c Substitution If a = b, then a may be substituted for b in any equation.
  • 4. Number Lines Real numbers can be superimposed on a line to provide coordinates of points. A point is selected as the starting point, or origin. Numbers to the left or the origin are negative, to the right positive. A B C D -2 -1 0 1 2 3
  • 5. Distance on a Number Line The distance between points is found by taking the positive difference in their coordinates Length (distance) A(Xa) to B (Xb) d = AB = | Xb Xa | Absolute value | a | Means to take what ever is inside and make it positive |8|=8 | -8 | = 8
  • 6. Segments and Bteweenness B is between A and C if it is on the same line and to the right of one, and to the left of the other. For any B between A and C, segment addition: A B C AB + BC = AC For endpoints A and B, the Midpoint (M): M = 1/2(A + B)
  • 7. References Glencoe: Geometric Concepts and Applications Section 2.1 and 2.2