Proving Statements about Segments

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Presentation transcript:

Proving Statements about Segments Textbook 2.5

Properties of Segment Congruence Reflexive: For any segment AB, AB = AB. Symmetric: If AB = CD, then CD = AB. Transitive: If AB = CD, and CD = EF, then AB = EF. ~ ~ ~ ~ ~ ~

Proof ~ ~ ~ Given UV = XY, VW = WX, WX = YZ Prove UW = XZ ~ STATEMENTS REASONS ~ ~ ~ 1. UV = XY, VW = WX, WX = YZ Given 2. VW = YZ ~ Transitive Property of Segment Congruence 3. UV = XY, VW = YZ Definition of Congruent Segments 4. UV + VW = XY + YZ Addition Property of Equality 5. UV + VW = UW, XY + YZ = XZ Segment Addition Postulate 6. UW = XZ Substitution Property of Equality 7. UW = XZ ~ Definition of Congruent Segments

Homework Page 105 – 107 6 – 18, 21, 22, 28 – 40 (even) (You can work on this in class on Friday along with the assignment given to the substitute. We will answer questions on Monday, and grade on Tuesday.)