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Understanding Postulates and Geometric Conjectures in Geometry

This lesson covers the fundamental postulates of geometry, including the definitions and relationships of geometric figures. Students will learn to validate conjectures about geometric objects, using counter-examples as well as inductive and deductive reasoning. Key concepts include the definitions of lines and planes formed by points, the validity of geometric conjectures, and how to critique arguments presented by others. The assignment will provide practical applications of the discussed postulates, enhancing student understanding of geometric properties.

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Understanding Postulates and Geometric Conjectures in Geometry

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  1. Lesson 1-3 Postulates

  2. Ohio Content Standards:

  3. Ohio Content Standards: • Formally define geometric figures. • 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. • Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, and inductive and deductive reasoning.

  4. Review:

  5. Review: • Postulate 1-1 :

  6. Review: • Postulate 1-1 : • Two points determine a unique line.

  7. Review: • Postulate 1-2 :

  8. Review: • Postulate 1-2 : • If two distinct lines intersect, then their intersection is a point.

  9. Review: • Postulate 1-3 :

  10. Review: • Postulate 1-3 : • Three noncollinear points determine a unique plane.

  11. As shown below, points K, L, and M are noncollinear. K M L

  12. As shown below, points K, L, and M are noncollinear. • Name all of the different lines that can be drawn through these points. K M L

  13. As shown below, points K, L, and M are noncollinear. • Name all of the different lines that can be drawn through these points. • Name the intersection of KL and KM. K M L

  14. Name all of the planes that are represented in the prism. Name all of the planes that are represented in the prism. A B E F C D G H

  15. Review:

  16. Review: • Postulate 1-4 :

  17. Review: • Postulate 1-4 : • If two distinct planes intersect, then their intersection is a line.

  18. The figure shows the intersection of six planes. G F H E C D B A

  19. The figure shows the intersection of six planes. G F H E C D B A Name the intersection of plane ABC and plane DEF.

  20. Assignment: Pgs. 21 & 22 10-30 evens

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