Properties and charts
1. Linear Pair Property
If two angles form a linear pair, then they are supplementary.
Algebraic Properties of Equality
Let a, b, and c be real numbers or expressions representing real numbers.
Addition Property
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If a = b, then a + c = b + c
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Subtraction Property
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If a = b, then a - c = b - c
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Multiplication Property
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If a = b, then ac = bc
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Division Property
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If a = b, then a/c = b/c
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Substitution Property
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If a = b, you may relace a with b in any true equation containing a and the resulting equation will still be true.
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If equals are added to equals, then the wholes are equal.
Proof:
x - 4 = 12 given statement of equality.
x - 4 + 4 = 12 + 4 Addition property of equalities
(4's , equal numbers, are added to equals, the sides of the equation.)
x = 16 Simplify
(x is a variable representing a whole number, 16 is a whole number)
Equivalence Properties of Equalities
Reflexive Property
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For any real number a, a = a.
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Symmetric Property
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For all real numbers a and b, if a =b, then b = a.
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Transitive Property
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For all real numbers a, b, and c, if a = b and b = c, then a = c.
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Equivalence Properties of Congruence
Reflexive Property
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Figure A is congruent to figure A
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Symmetric Property
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If figure a is congruent to figure b, then figure b is congruent to figure a.
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Transitive Property
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If figure a is congruent to figure b, and figure b is congruent to figure c, then figure a is congruent to figure c.
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Three-dimensional chart for determining octant positions.
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-
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0
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x
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front
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back
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y-z plane
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y
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right
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left
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x-z plane
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z
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top
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bottom
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x-y plane
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Consider the point ( 3, 1, 7). All three are positive; therefore the point is located in the top, front, right octant or the "first octant."
Consider the point (4, 0, -2). The y coordinate is 0; therefore, the point lies on the x-z plane.
Consider the point (-8, -1, -5) All three are negative; therefore, the point is located in the bottom, back, left octant.
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