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Section 2.3

Section 2.3. Structure of Geometry. Definitions. Postulate(axiom) - is a statement accepted without proof Theorem -is a statement that is proven by using defs , postulates, or previously proven theorems. Postulates:.

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Section 2.3

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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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