  We survey the status of decidabilty of the consequence relation in various
axiomatizations of Euclidean geometry. We draw attention to a widely overlooked
result by Martin Ziegler from 1980, which proves Tarski's conjecture on the
undecidability of finitely axiomatizable theories of fields. We elaborate on
how to use Ziegler's theorem to show that the consequence relations for the
first order theory of the Hilbert plane and the Euclidean plane are
undecidable. As new results we add: (A) The first order consequence relations
for Wu's orthogonal and metric geometries (Wen-Ts\"un Wu, 1984), and for the
axiomatization of Origami geometry (J. Justin 1986, H. Huzita 1991)are
undecidable.
  It was already known that the universal theory of Hilbert planes and Wu's
orthogonal geometry is decidable. We show here using elementary model theoretic
tools that (B) the universal first order consequences of any geometric theory
$T$ of Pappian planes which is consistent with the analytic geometry of the
reals is decidable.
