Download 25 Reason Using Properties from Algebra

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Reason Using Properties from Algebra
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Properties of Equality: Let a, b, and c be real numbers Addition Property: If a=b, then a+c = b+c
example: x­3=7
x­3+3=7+3
Subtraction Property: If a=b, then a­c = b­c
example: y+5=11
y+5­5=11­5
Multiplication Property: If a=b, then ac = bc
example: 1 z = 6
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1 z 4 = 6 4
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Division Property: If a=b and c≠0, then a÷c=b÷c
example: 8x =16
8x = 16
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Substitution Property: If a=b, then a may be substituted for b in any equation or expression.
example: x = 7
2x + 4 = 2(7) + 4
Distributive Property: a(b + c) = ab + ac, where a, b, and c are real numbers.
example: 2(x + 3) = 2x + 6
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Reflexive Property: For any real number a, a=a
Symmetric Property: If a=b then b=a
Transitive Property: If a=b and b=c, then a=c
Examples:
1.) 3x +8 = 14
3x = 6
x = 2
2.) ­5(7­4m) = 7 ­ 8m
­35 + 20m = 7­ 8m
20m = 42 ­ 8m
28m = 42
m = 3
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3.) ½(x+6) = x+1
4.) Show that CF = AD
A
B
C
D
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Equation
1.) AB = _____
2.) BC = _____
3.) AC = AB + BC
4.) DF = ___ + ___
5.) DF = BC + AB
6.) DF = ___
7.) DF+CD=___+CD
8.) CD + DF = CF
AC + CD = AD
9.) ___ = ___
F
Reason
1.) Given
2.) Given
3.) ________
4.) Segment Addition
Postulate
5.) _______ Property of Equality.
6.) _______ Property of Equality.
7.) _______ Property of Equality.
8.) ________ Postulate
9.) Substitution Property of Equality.
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Name the property of equality that the statement illustrates.
5.) If GH = JK, then JK = GH.
6.) If r = s, and s = 44, then r = 44.
7.) m<N = m<N
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Homework:
p. 108­111/1­25 Odd
(If it is a proof, both sides must be shown)
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