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Reasoning In Algebra

Reasoning In Algebra. Properties of Equality are accepted as true and are used to deductively prove conditional statements. Properties of Equality page 89. Addition Property Subtraction Property Multiplication Property Division Property Reflexive Property: a = a

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Reasoning In Algebra

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  1. Reasoning In Algebra Properties of Equality are accepted as true and are used to deductively prove conditional statements.

  2. Properties of Equality page 89 • Addition Property • Subtraction Property • Multiplication Property • Division Property • Reflexive Property: a = a • Symmetric Property: If a = b, then b = a. • Transitive Property: If a = b and b = c, then a = c. Try 32 - 37

  3. More Properties • Substitution is a more general form of the Transitive Property of Equality: If a = b, then “a” can replace “b” in any expression. • Distributive Property: a(b + c) = ab + ac

  4. Example 1 and Check Understanding 1 • Give a reason for each step: • Ray LM bisects >KLN • m<MLN = m<KLM • 4x = 2x + 40 • 2x = 40 • x = 20

  5. Example 2 and Check Understanding 2 • Find AB and BC by substituting y = 6 in the expressions. Check that AB + BC = 21

  6. Properties of Congruence • Reflexive Property: Figures are congruent to themselves. <A <A • Symmetric Property: If AB BC, then BC AB • Transitive Property: • If <A <B and <B <C, then <A <C

  7. Example 3 and Check Understanding 3 • Name that Property: • XY XY • If m<A = 45 and 45 = m<B, then m<A = m< B

  8. Evens, 2-24 • #2:Name that Reason! • XZ + ZY = XY • 3(n+4) + 3n = 42 • 3n + 12 + 3n =42 • 6n + 12 = 42 • 6n = 30 • n = 5

  9. Practice Makes Perfect! • #4: Name that Reason! • 5(x + 3) = -4 • 5x + 15 = -4 • 5x = -19 • x = -19/5

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