Download Properties from Algebra

2-2 Properties from Algebra
Notes on worksheet
Properties from Algebra
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See Worksheet!
Addition Property
Subtraction Property
Multiplication Property
Division Property
You can +/-/x/÷ the
same number on
both sides of an
equation
Properties from Algebra
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Substitution: think “replace”
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Ex: a+b=c, if c = 8 then a + b = 8
Questions on Substitution???
We use this ALOT in Proofs!
Reflexive: a # equals itself (same on both side)
Symmetric: switch the side of the equal sign it is on
Transitive (3 parts)
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Ex: 6 + 4 = 10
5 • 2 = 10
6+4=5•2
Properties from Algebra
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Properties of Congruence: Properties of
Equality where the equal sign is replaced
with a congruency sign.
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Distributive Property
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If a(b + c), then ab + ac
What do you notice about all the properties?
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They are If-Then statements!
Example
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Justify the statement:
If WX = YZ, then WY = XZ
addition: we added the segment
XY to both sides of the
original equation
W
X
Y
Z
Example
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Justify the statement:
If WY = XZ, then WX = YZ
subtraction: we subtracted the
segment XY from both
sides of the original
equation
W
X
Y
Z
TOO—on Whiteboards!!!!
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If 4x = -24, then x = -6
DIVISION!
If a = b and b = c then a = c.
Transitive!
Angle A = Angle A
Reflexive!
Homework
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Worksheet 2-1 and 2-2
Skip #14 the Proof, We will do it together
tomorrow