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2.4 Use Postulates & Diagrams

2.4 Use Postulates & Diagrams. Objectives: To illustrate and understand postulates about lines and planes To accurately interpret geometric diagrams. Postulates.

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2.4 Use Postulates & Diagrams

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  1. 2.4 Use Postulates & Diagrams Objectives: • To illustrate and understand postulates about lines and planes • To accurately interpret geometric diagrams

  2. Postulates This chain of logical reasoning must begin somewhere, so every deductive system must contain some statements that are never proved. In geometry, these are called postulates.

  3. Postulates and Theorems • Postulates are statements in geometry that are so basic, they are assumed to be true without proof. • Sometimes called axioms. • Theorems are statements that were once conjectures but have since been proven to be true based on postulates, definitions, properties, or previously proven conjectures. Both postulates and theorems are ordinarily written in conditional form.

  4. Postulates 1 - 4 Postulate 1: Ruler Postulate Pg 9 Postulate 2: Segment Addition Postulate Pg 10 Postulate 3: Protractor Postulate Pg 24 Postulate 4: Angle Addition Postulate Pg 25

  5. Postulates 5 - 11

  6. Example 1 State the postulate illustrated by the diagram.

  7. Example 2:Identify postulates from a diagram • Use the diagram to write examples of Postulates 9 and 11. • Postulate 9:Plane Q contains at least three noncollinear points, W, V, and Y. • Postulate 11:The intersection of plane P and plane Q is line b.

  8. Use the diagram to write examples of Postulates 9 and 10. Postulate 9: Plane Pcontains at least three noncollinear points, A, B, and C. Postulate 10: Point Aand point Blie in plane P, so line ncontaining Aand Balso lies in plane P.

  9. Use the diagram to write examples of Postulates 6 and 8 P6:Line l contains at least two points R and S Postulate 8: Through noncollinear points R, S, and W, there exists exactly one plane M

  10. Use the diagram to write examples of Postulates 5 and 7 Which postulates are shown in the following diagram?

  11. Checkpoint • Using the diagram, which postulate allows you to say that the intersection of line a and line b is a point? • Postulate 7

  12. Interpreting Diagrams When you interpret a diagram, you can assume only information about size or measure if it is marked.

  13. Interpreting Diagrams

  14. Interpreting Diagrams

  15. Perpendicular Figures A line is perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.

  16. Example Which of the following cannot be assumed from the diagram? • A, B, and F are collinear. • E, B, and D are collinear. • AB  plane S

  17. Example Which of the following cannot be assumed from the diagram? • CD  plane T • AF intersects BC at point B.

  18. Assignment Pg 99 # 3 – 23 (# 11-13, don’t give real world example. If false, draw a picture of a counterexample)

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