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## Lesson 2-7

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**Lesson 2-7**Proving Segment Relationships**Ohio Content Standards:**Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.**Ohio Content Standards:**Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.**Ohio Content Standards:**Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.**Postulate 2.8Ruler Postulate**The points on any line or line segment can be paired with real numbers so that, given any two points A and B on a line, A corresponds to zero, and B corresponds to a positive real number.**Postulate 2.9Segment Addition Postulate**If B is between A and C, then AB + BC = AC.**Postulate 2.9Segment Addition Postulate**If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.**Theorem 2.2Segment Congruence**Congruence of segments is reflexive, symmetric, and transitive. .**Theorem 2.2Segment Congruence**Congruence of segments is reflexive, symmetric, and transitive. Reflexive Property AB AB .**Theorem 2.2Segment Congruence**Congruence of segments is reflexive, symmetric, and transitive. Symmetric Property If AB CD, then CD AB. .**Theorem 2.2Segment Congruence**Congruence of segments is reflexive, symmetric, and transitive. Transitive Property If AB CD, and CD EF, then AB EF. .**Prove the following.Given: WY = YZ YZ XZ XZ**WXProve: WX WY 3 cm Y Z 3 cm W X