Question

List the differences and similarities of SMSG Axioms with neutral geometry.

Answer 1

Simibritter of somsg aitons with rental quarting 1) Given any a distact points there is exactly One Une that contains ther. There exists a unique positive number to every pain of of distinct points there a n d this worker is called the distance between two points and it is Distance postalate kaler Axiom - Every line has a coordinate faction. Every plane contains atleast 3 non collinear points. v plane seperation Ariam Given a line and a place containing it, the points of the plane that de not lie on the line form two sets such that? a) Each of the sets is conven b) If p is in one set and a is in other, the segment pa intersects the line Angle measurement trion vil Angle construction postulale VT) Angle measurement addition Axiom SAs portulate DOOR

26 Differences - 1 In neutral geometry, there exists three lines that are not concurrent- 1) In neutral geometry, for every point & there exists a line that does not pass through P. i) In suso axions, it a points lie in a plane then the line containing these points lies in the same plane. 2) In smsa anions, if a planes intersect, then that intersection is a line- In smsg axioms if two triangles are congruent, then the triangular regions have the same area 7 In smsGariom, the volume of a rectangle parallelpiped es equal to the product of the length of its attitude and area of its base TLD Voleme