MAT 141
Sample Final
1) (4 Points) True or False:
a: Hilbert’s axiom of parallelism is the same as the Eu-
clidean parallel postulate.
b: One of the congruence axioms is the side-angle-side
(SAS) criterion for congruence of triangles.
c: Euclidean geometry is as true today as it was 2300 years
ago.
d: Euclid’s parallel postulate always holds.
2) (4 Points) Use ruler and compass to find the center of a
circle.
3) (4 Points) Explain, using anything you know, why the
construction in Problem 2 yields the desired result.
4) (4 Points) Invent a model for incidence geometry that has
neither the elliptic, hyperbolic nor the Euclidean parallel
properties.
5) (4 Points) Assume that the incidence axioms hold and
that there are infinitely many points. Prove that either
there are infinitely many lines or there is a line incident to
infinitely many points.
6) (4 Points) Consider the Cartesian plane with the origin
removed. Interpret points, lines, measurement of segments
and angles in the usual ways. Which of the 13 Hilbert plane
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