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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 2Proof With Segment Congruence OBJECTIVE: To write proofs involving segment congruence (2.9.8J) (M8.D.1.1)

KEY CONCEPT: Theorem 2.2: Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. REFLEXIVE PROPERTY: SYMMETRIC PROP: If then TRANSITIVE PROP: If and, then

Example 7-2a Prove the following. Prove: Given:

Example 7-2b 1. Given Definition of congruent segments Given Transitive Property Transitive Property 5. Proof: Statements Reasons

Example 7-2c Prove the following. Prove: Given:

Example 7-2d Proof: Statements Reasons 1. Given 2. Transitive Property 3. Given 4. Transitive Property 5. Symmetric Property

REVIEW Justify each statement with a property If, then 3.GIVEN: PROVE: Statements (Reasons). a. (Given) b.PQ = RS, QS = ST c.PS = PQ + QS, RT = RS + ST d. (Add. Prop.) e. (Substitution) f. Reflexive Symmetric Def. Of congruent segs. Seg. Add. Post. PQ + QS = RS + ST PS = RT Def. Of congruent segs.

End of Lesson 7

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