  We probe the principle of complementarity by performing a double-slit
experiment based on entangled photons created by spontaneous parametric
down-conversion from a pump mode in a TEM01-mode. Our setup brings out the need
for a careful selection of the signal-idler photon pairs for our study of
visibility and distinguishability. Indeed, when the signal photons interfering
at the double-slit belong to this double-hump mode we obtain almost perfect
visibility of the interference fringes and no "which-slit" information is
available. However, when we break the symmetry between the two maxima of the
mode by detecting the entangled idler photon, the paths through the slits
become distinguishable and the visibility vanishes. It is the mode function of
the photons selected by the detection system which decides if interference, or
"which-slit" information is accessible in the experiment.
