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Understanding Geometric Foundations: Postulates and Theorems

This section explores the fundamental concepts of geometry, focusing on definitions, postulates, and theorems. A postulate (axiom) is a statement accepted without proof, while a theorem is proved through definitions, postulates, or previously established theorems. Key postulates covered include the Ruler Postulate, which defines the distance between points, and the Segment Addition Postulate, which illustrates that if point B is between A and C, then AB + BC = AC. Additional insights include the Protractor Postulate and the Angle Addition Postulate, essential for measuring angles in geometry.

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Understanding Geometric Foundations: Postulates and Theorems

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  1. Section 2.3 Structure of Geometry

  2. Definitions • Postulate(axiom)- is a statement accepted without proof • Theorem-is a statement that is proven by using defs, postulates, or previously proven theorems

  3. Postulates: • Ruler Postulate- the pts on a # line can be paired 1:1 with the set of reals #’s(coords) and the distance between any 2 pts = │diff of their coords│ Ex: A B -6 4 d AB= │-6 – 4 │= 10 units

  4. Example : • Find the distance from A to B: A B 3 8 AB = │8 – 3 │= 5

  5. Segment Addition Postulate- Pts A, B, & C are collinear and B is in between A & C, then AB + BC = AC( 2parts sum= whole) If B is between A and C, then AB + BC = ACA B C

  6. Find 1. RS 2. QS 3. TS 4. TV

  7. Protractor Postulate- the rays of a given angle can be paired 1:1 on the protractor and the measure is determined by: │diffs of those real #’s│

  8. Angle addition Postulate- If C is in the interior of <AOD, then m<AOC + m<COD = m<AOD.

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