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Lesson 2-7 Proving Segment Relationships Ohio Content Standards: 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 twodimensional figures and threedimensional 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 2.8 Ruler Postulate Postulate 2.8 Ruler 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 2.9 Segment Addition Postulate Postulate 2.9 Segment Addition Postulate If B is between A and C, then AB + BC = AC. 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. Prove the following. Given: PR = QS Prove: PQ = RS P Q R S Theorem 2.2 Segment Congruence Theorem 2.2 Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. . Theorem 2.2 Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Reflexive Property AB . AB Theorem 2.2 Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Symmetric Property If AB CD, then CD AB. . Theorem 2.2 Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Transitive Property If AB CD, and CD EF, then AB EF. . Prove the following. 3 cm Given: WY = YZ YZ XZ XZ WX Prove: WX WY Y Z 3 cm W X Assignment: Pgs. 104 - 106 12-20 all, 32-44 evens