Proving Statements about Segments

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Presentation transcript:

Proving Statements about Segments Chapter 2 Section 2.5 Proving Statements about Segments

Warm-Up

Properties of Segment Congruence Segment congruence is reflexive, symmetric, and transitive Reflexive: Symmetric: Transitive: Theorem: A true statement that follows as a result of other true statements. Theorems must be proved true

Match the statement with the Property of Congruence Reflexive Property of congruence Transitive Property of congruence Symmetric Property of congruence

Mark the diagram with the given information

Mark the diagram with the given information

1. Given 2. Given 3. Substitution 4. Definition  Segments 5. Given 6. Transitive

1. Given 2. Reflexive 3. Addition 4. Segment Addition 5. Segment Addition 6. Substitution

Paragraph Proof: When a proof is written in paragraph form. Since AL = SK and by reflexive property LS = LS, from the addition property of equality it follows that AL + LS = SK + LS. Also by segment addition postulate we can say that AL + LS = AS and SK + LS = LK. Thus a simple substitution allows us to arrive at AS = LK You may use any proof style (two-column or paragraph) at anytime on any assignment.