Question

Prove that the axiomatic set for Fano's 7 point/line geometry is independent.

Answer #1

Prove that the SMSG axiomatic set is not independent.
I post this question again because last time your guy did not
answer correct this question. Please help me !

Prove (with neutral geometry)
If the angle of parallelism for a point P and a line RS is
Less Than 90 degrees, then there exist At Least Two lines through P
that are parallel to line RS.
Please explain step by step and include a diagram. Thanks so
much!

Consider the following axiomatic system: 1. Each point is
contained by precisely two lines. 2. Each line is a set of four
points. 3. Two distinct lines that intersect do so in exactly one
point.
True or false? There exists a model with no parallel lines.

(Euclidean and Non Euclidean geometry)
Consider the following statements:
Given a line l and a point P not on the line:
There exists at least one line through P which is
perpendicular to l.
There exists at most one line through P which is
perpendicular to l.
There exists exactly one line through P which is
perpendicular to l.
Prove each statement or give a
counter-example E2 (Euclidean Plane), H2 ,
(Hyperbolic Plane)and the sphere S2 (Spherical
Plane)
( Consider...

prove that rectangles dont exist in hyperbolic geometry

Consider an axiomatic system that consists of elements in a set
S and a set P of pairings of elements (a, b) that satisfy the
following axioms:
A1 If (a, b) is in P, then (b, a) is not in P.
A2 If (a, b) is in P and (b, c) is in P, then (a, c) is in
P.
Given two models of the system, answer the questions below.
M1: S= {1, 2, 3, 4}, P= {(1, 2), (2,...

prove that the product of a rotation and a translation is a
rotation
Euclidean Geometry and Transformatons

given a line AB and a point C not on AB, prove that there is a
Ray AD such that AC is between AB and AD

Describe the Saccheri Quadrilateral and prove in neutral
geometry that the summit angles are congruent.

Prove the HL (hypotenuse-leg) congruence property for right
triangles as a theorem in Absolute Geometry.

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