Chapter 2: Reasoning & Proof 2.4 Reasoning in Algebra.

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Presentation transcript:

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 (subtracting the same number from both sides of an equation does not change the equation!)

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!)

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

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

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

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

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

Distributive Property a(b + c) = ab + ac Example: 2x(x + 3) =

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

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

Quick check 1 Fill in each missing reason. Given: LM bisects angle KLN LM bisects angle KLNGiven Definition of angle bisector 4x = 2x x = 40 X = 20

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