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Chapter 2: Reasoning & Proof

Chapter 2: Reasoning & Proof. 2.4 Reasoning in Algebra. Properties of Equality. Addition Property If a = b, then a + c = b + c (adding the same number to both sides of an equation does not change the equation!). Properties of Equality. Subtraction Property If a = b, then a – c = b – c

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Chapter 2: Reasoning & Proof

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  1. Chapter 2: Reasoning & Proof 2.4 Reasoning in Algebra

  2. Properties of Equality • Addition Property If a = b, then a + c = b + c (adding the same number to both sides of an equation does not change the equation!)

  3. Properties of Equality • Subtraction Property If a = b, then a – c = b – c (subtracting the same number from both sides of an equation does not change the equation!)

  4. Properties of Equality • Multiplication Property: If a = b, then a · c = b · c (Multiplying both sides of an equation by the same number does not change the equation!)

  5. Properties of Equality • Division Property: If a = b and c ≠ 0, then (Dividing both sides by the same number does not change the equation!)

  6. Properties of Equality • Reflexive Property: a = a (ANYTHING always equals itself!)

  7. Properties of Equality • Symmetric Property: If a = b, then b = a.

  8. Properties of Equality • Transitive Property: If a = b and b = c, then a = c.

  9. Properties of Equality • Substitution Property: If a = b, then b can replace a in any expression.

  10. Distributive Property • a(b + c) = ab + bc • Example: • 2x(x + 3) =

  11. Example 1 • Solve for x and justify each step. • Given:

  12. Example 2 • Solve for y and justify each step. • Given: AC = 21

  13. Quick check 1 • Fill in each missing reason. • Given: LM bisects angle KLN

  14. Example 3 • Name the property of equality or congruence that justifies each statement: • If 2x – 8 = 10, then 2x = 18. • If and , then • If , then

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