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Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates, and theorems.
Remarks
Example: Classify each of the following as an undefined term, defined term, postulate, or theorem:- Line
- Isosceles triangle
- Regular hexagon
- Pythagorean Therom
Students should also explore non-Euclidean geometries including hyperbolic and elliptic geometries.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
Idea: Level 3: Strategic Thinking & Complex Reasoning
Standard: Mathematical Reasoning and Problem Solving - In a general sense, mathematics is problem solving. In all mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results. At this level, apply these skills to making conjectures, using axioms and theorems, constructing logical arguments, and writing geometric proofs. Learn about inductive and deductive reasoning and how to use counterexamples to show that a general statement is false.
Date Adopted or Revised: 09/07
Content Complexity Rating:
Level 3: Strategic Thinking & Complex Reasoning
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More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
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