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Contents Lesson 2-1Inductive Reasoning and Conjecture Lesson 2-2Logic Lesson 2-3Conditional Statements Lesson 2-4Deductive Reasoning Lesson 2-5Postulates and Paragraph Proofs Lesson 2-6Algebraic Proof Lesson 2-7Proving Segment Relationships Lesson 2-8Proving Angle Relationships

Lesson 7 Contents Example 1Proof With Segment Addition OBJECTIVE: To write proofs involving segment addition (2.9.8J) (M8.D.1.1)

Key Concept: POSTULATE 2.8 – Ruler Postulate The points on any line or line segment can be paired with real numbers so that, given any 2 points A and B on a line, A corresponds to zero, and B corresponds to a positive real number.

Key Concept: POSTULATE 2.9: Segment Addition Postulate. If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.

Example 7-1a Given: PR = QS Prove the following. Prove: PQ = RS 1. Given PR = QS Subtraction Property PR – QR = QS – QR Segment Addition Postulate PR – QR = PQ; QS – QR = RS Substitution PQ = RS 4. Proof: Statements Reasons

Example 7-1b Prove the following. Prove: Given:

Example 7-1c Proof: Statements Reasons 1. Given 2. Transitive Property 3. Given 4. Addition Property AC = AB, AB = BX AC = BX CY = XD AC + CY = BX + XD 5. Segment Addition Property AC + CY = AY; BX + XD = BD AY = BD 6. Substitution

REVIEW Justify with a property: 1.If AB = AC + CB, then AB – AC = CB 2.If m  P + m  Q = 110 and m  R = 110, then m  P + m  Q = m  R. 3.If x(y + z) = a, then xy + xz = a. 4.If n –17 = 39, then n = If cv = md and md = 15, then cv = 15. Subtraction Substitution Dist. Prop. Add. Prop. Trans. Prop.

End of Lesson 7

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