Algebraic Proof

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Algebraic Proof

• AdditionIf a b, then a c b c.
• SubtractionIf a b, then a - c b - c.
• Multiplication If a b, then ca cb.
• Division If a b, and c ? 0, then a ? c b ? c

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Algebraic Proof

• Substitution If a b c and b d, then a d
  c.
• Reflexive a a.
• Symmetric If a b, then b a.
• Transitive If a b and b c, then a c.
• Distributive a(b c) ab ac.

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Algebraic Proof

• Deductive Argument A proof formed by a group of
  algebraic steps used to solve problems.
• Since geometry also uses variables, numbers, and
  operations, many of the properties of equality
  used in algebra are also true in geometry.
  (Examples segment measures, angle measures)

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Algebraic Proof

• Two-column proof (formal proof) A form of
  deductive argument with statements and reasons
  organized in two-columns.
• Each step that advances the argument is called a
  statement.
• Each property, definition, rule, etc used to
  justify the statements are called reasons.

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Example 6-1c
Algebraic Steps Properties
Original equation
Distributive Property
Substitution Property
Subtraction Property
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Example 6-1d
Substitution Property
Division Property
Substitution Property
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Example 6-2f
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Example 6-2g
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Example 6-3d
Answer C
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Example 6-4b
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Example 6-4c