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Lesson 2-7

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  1. Lesson 2-7 Proving Segment Relationships

  2. Ohio Content Standards:

  3. 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.

  4. Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

  5. 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.

  6. Postulate 2.8Ruler Postulate

  7. 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.

  8. Postulate 2.9Segment Addition Postulate

  9. Postulate 2.9Segment Addition Postulate If B is between A and C, then AB + BC = AC.

  10. 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.

  11. Prove the following.Given: PR = QSProve: PQ = RS P Q R S

  12. Theorem 2.2Segment Congruence

  13. Theorem 2.2Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. .

  14. Theorem 2.2Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Reflexive Property AB AB .

  15. Theorem 2.2Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Symmetric Property If AB CD, then CD AB. .

  16. Theorem 2.2Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Transitive Property If AB CD, and CD EF, then AB EF. .

  17. Prove the following.Given: WY = YZ YZ XZ XZ WXProve: WX WY 3 cm Y Z 3 cm W X

  18. Assignment:Pgs. 104 - 106 12-20 all, 32-44 evens