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Proving Segment Relationships in Geometry: Ohio Content Standards Overview

This lesson focuses on proving segment relationships in geometry according to Ohio Content Standards. Students will learn how to establish the validity of conjectures involving geometric objects and their properties using various reasoning methods, including counter-examples, inductive and deductive reasoning, as well as critiquing the arguments of others. Key concepts include the Ruler Postulate, Segment Addition Postulate, and the Segment Congruence Theorem. Students will engage in practice problems to enhance their understanding of these geometric principles.

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Proving Segment Relationships in Geometry: Ohio Content Standards Overview

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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

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