Download 2-4 Reasoning in Algebra

2-4 Reasoning in Algebra
Objectives:
• Use basic properties of algebra in
reasoning
• Define congruence
• State the properties of congruence
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Properties of Equality
Addition Property
If a = b, then a + c = b + c
Subtraction Property
If a = b, then a – c = b – c
Multiplication Property
If a = b, then a * c = b * c
Division Property
If a = b and c ≠ 0, then a/c = b/c
Reflexive Property
a=a
Symmetric Property
If a = b, then b = a
Transitive Property
If a = b and b = c, then a = c
Substitution Property
If a = b, then b can replace a in
any expression
Distributive Property
a(b + c) = ab + ac
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Solve and Write a Justification for Each Step
2 (x + 1) = 8 Given
2x + 2 = 8
Distributive Property
2x
=6
Subtraction Property of =
x
=3
Division Property of =
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Congruence in Geometry
• Congruence – Having the same shape
and size
• Symbol for congruence ≅
• AB ≅ CD (Segment AB is congruent to
segment CD.)
A
B
C
D
•∠ A ≅ ∠ B (Angle A is congruent to angle
B.)
A
B
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Properties of Congruence
• Reflexive Property
AB ≅ AB
∠A≅∠A
• Symmetric Property
If AB ≅ CD, then CD ≅ AB
If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A
• Transitive Property
If AB ≅ CD and CD ≅ EF, then AB ≅ EF
If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C,then ∠ A ≅ ∠ C
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