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Proofs!!!

Proofs!!!. Ok just little ones :). Properties of Equality. Addition Property (APOE) If a = b, then a + c = b + c Subtraction Property (SPOE) If a = b, then a - c = b - c Multiplication Property (MPOE) If a = b, then a * c = b * c Division Property (DPOE) If a = b and c ≠ 0, then.

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Proofs!!!

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  1. Proofs!!! Ok just little ones :)

  2. Properties of Equality • Addition Property (APOE) • If a = b, then a + c = b + c • Subtraction Property (SPOE) • If a = b, then a - c = b - c • Multiplication Property (MPOE) • If a = b, then a * c = b * c • Division Property (DPOE) • If a = b and c ≠ 0, then

  3. Properties Of Equality • 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

  4. Distributive Property • If a(b + c) = ab + ac • If a(b - c) = ab - ac

  5. Properties of Congruence • Definition of Congruence • To move between and equal sign (=) and a congruency sign (≅) you use the • Def of ≅ • Note : Properties of equality can only be used with =

  6. Reflexive Property of ≅ • Symmetric Property of ≅ • Transitive Property of ≅

  7. Identify the Property Used • 1.) 2x + 9 = 19, then 2x = 10 • SPOE • 2.) • Transitive POC • 3.) • Symm POE

  8. You Try 4.) 5.) 6.) 7.) 1.) Symm POC 2.) Distributive 3.) MPOE 4.) Ref POE

  9. Algebra Proofs

  10. Algebra Proof

  11. Justify Step When solving an equation • What is the value of x? Justify each step.

  12. You Try • What is the value of x? Justify

  13. Proofs! • A two - Coolum proof is set up with a statements Coolum and a reason Coolum. Each statement follows logically from the above statements.

  14. The End

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