4. Consider the four-point geometry described by the following axioms.Undefined terms: point, line, on.Axiom 1. There exist exactly four points.Axiom 2. Two distinct points are on exactly one line.Axiom 3. Each line lies on exactlu two noints.d. Is Axiom 3 inaepenaent or Axioms 1 and 2?e. Is the system complete? Why or why not?f. "Every line contains at most two points". Is the statement True or False. Justify your answer.g. Obtain an axiomatic system for four-point geometry by dualizing the axioms. (Just state theaxioms)

d) Axiom 3 is not independent, it reflects the fact that out of the given four points, only two can…

4. Consider the four-point geometry described by the following axioms. Undefined terms: point, line, on. Axiom 1. There exist exactly four points. Axiom 2. Two distinct points are on exactly one line. Axiom 3. Each line lies on exactlu two noints. d. Is Axiom 3 inaepenaent or Axioms I and 2? e. Is the system complete? Why or why not? f. "Every line contains at most two points". Is the statement True or False. Justify your answer. g. Obtain an axiomatic system for four-point geometry by dualizing the axioms. (Just state the axioms)

4. Consider the four-point geometry described by the following axioms. Undefined terms: point, line, on. Axiom 1. There exist exactly four points. Axiom 2. Two distinct points are on exactly one line. Axiom 3. Each line lies on exactlu two noints. d. Is Axiom 3 inaepenaent or Axioms I and 2? e. Is the system complete? Why or why not? f. "Every line contains at most two points". Is the statement True or False. Justify your answer. g. Obtain an axiomatic system for four-point geometry by dualizing the axioms. (Just state the axioms)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.2: Similar Polygons

Problem 11E: a Does the similarity relationship have a reflexive property for triangles and polygons in general?...

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