Reasoning in Algebra Chapter 2: Reasoning and Proof1 Objectives 1 To connect reasoning in algebra and geometry.

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Presentation transcript:

Reasoning in Algebra Chapter 2: Reasoning and Proof1 Objectives 1 To connect reasoning in algebra and geometry

Addition Property If a = b, then a + c = b + c. Subtraction Property If a = b, then a – c = b – c. Multiplication Property If a = b, then a · c = b · c. Division Property If a = b and c ≠ 0, then Reasoning in Algebra Chapter 2: Reasoning and Proof2 Key Concepts Properties of Equality

Reasoning in Algebra Chapter 2: Reasoning and Proof3 Key Concepts Properties of Equality continued 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.

The Distributive Property a(b + c) = ab + ac Reasoning in Algebra Chapter 2: Reasoning and Proof4 Key Concepts

Reasoning in Algebra Chapter 2: Reasoning and Proof5 Justify each step used to solve 5x – 12 = 32 + x for x. 1.5x = 44 + x 2.4x = 44 3.x = 11 Given: 5x – 12 = 32 + x

Reasoning in Algebra Chapter 2: Reasoning and Proof6 Suppose that points A, B, and C are collinear with point B between points A and C. Solve for x if AC = 21, BC = 15 – x, and AB = 4 + 2x. Justify each step. AB + BC=AC (4 + 2x) + (15 – x)= x=21 x=2x=2

Reasoning in Algebra Chapter 2: Reasoning and Proof7 Key Concepts Properties of Congruence

Reasoning in Algebra Chapter 2: Reasoning and Proof8 Name the property that justifies each statement. a.If x = y and y + 4 = 3x, then x + 4 = 3x. b.If x + 4 = 3x, then 4 = 2x.

Reasoning in Algebra Chapter 2: Reasoning and Proof9 (continued) c.If ∠ P ≅ ∠ Q, ∠ Q ≅ ∠ R, and ∠ R ≅ ∠ S, then ∠ P ≅ ∠ S