Download 6. The sum of angles in a triangle is =180° 7. The sum of angles in a

Neutral geometry: All axioms
except the fifth axiom (about
the number of parallel lines).
Could be proven(neutral
geometry):
1. SSS.
2. ASA.
3. SAS.
4. Pons Asinorum (about
angles of isoceles triangle).
5. The sum of two angles of a
triangle is < 180°
6. The sum of angles in a
triangle is ≤ 180°
7. The sum of angles in a
quadrilateral is ≤ 360°
8. We can always draw the
perpendicular line to the given
line through the given point
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Eucledian geometry=
neutral+ we can draw
only one line parallel to
the given line though the
given point
6. The sum of angles in a
triangle is =180°
7. The sum of angles in a
quadrilateral is = 360°
Hyprbolic geometry=
neutral+ we can draw
more than one line
parallel to the given line
though the given point
6. The sum of angles in a
triangle is <180°. (For
any number ε>0 there
exists a triangle with the
sum of angles <ε.)
7. The sum of angles in a
quadrilateral is < 360°
Other corollaries:
No rectangles.
No similar triangles.
There exist three non collinear
points such that it is impossible
to draw a circle through them.
Locus of points equidistant from
a line is not a line.