Download 1.3 Neutral Geometry

Neutral Geometry
Section 1.3
1.
Neutral Geometry – A plane geometry is neutral if it uses neither Euclid’s fifth
postulate nor its logical consequences.
Propositions 1 – 28 of Book 1 of the Elements make no reference (directly or indirectly)
of Euclid’s fifth postulate.
2.
Prove the following propositions of neutral geometry (without using the 5th axiom
or its logical consequences:
a)
If in a triangle two angles equal one another, then the sides opposite the equal
angles also equal one another
b)
Proposition 10 (State it)
c)
In any triangle, if one of the sides is produced then the exterior angle is greater
than either of the two interior and opposite angles.
d)
Every line segment has exactly one mid-point.
e)
Every angle has exactly one bisector.
f)
Supplements (or complements) of the same angle are congruent.
g)
Pasch’s Axiom.
h)
Crossbar Theorem.
i)
Equilateral triangles are also equiangular.