diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index 2dc4cae18266..4f8a55ec96ee 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -175,6 +175,9 @@ def update_from(self, other):
         self._us_dashes = other._us_dashes
         self.set_linewidth(other._linewidth)  # also sets dash properties
         self.set_transform(other.get_data_transform())
+        # If the transform of other needs further initialization, then it will
+        # be the case for this artist too.
+        self._transformSet = other.is_transform_set()
 
     def get_extents(self):
         """
@@ -585,14 +588,9 @@ def _update(self):
         if self.props is not None:
             self.update(self.props)
         else:
-            r, g, b, a = colors.to_rgba(self.patch.get_facecolor())
-            rho = 0.3
-            r = rho * r
-            g = rho * g
-            b = rho * b
-
-            self.set_facecolor((r, g, b, 0.5))
-            self.set_edgecolor((r, g, b, 0.5))
+            color = .3 * np.asarray(colors.to_rgb(self.patch.get_facecolor()))
+            self.set_facecolor(color)
+            self.set_edgecolor(color)
             self.set_alpha(0.5)
 
     def _update_transform(self, renderer):
diff --git a/lib/matplotlib/tests/test_patches.py b/lib/matplotlib/tests/test_patches.py
index da880df39874..f81e066046d4 100644
--- a/lib/matplotlib/tests/test_patches.py
+++ b/lib/matplotlib/tests/test_patches.py
@@ -5,15 +5,12 @@
 from numpy.testing import assert_almost_equal, assert_array_equal
 import pytest
 
-from matplotlib.patches import Polygon
-from matplotlib.patches import Rectangle
-from matplotlib.testing.decorators import image_comparison
+from matplotlib.patches import Polygon, Rectangle
+from matplotlib.testing.decorators import image_comparison, check_figures_equal
 import matplotlib.pyplot as plt
-import matplotlib.patches as mpatches
-import matplotlib.collections as mcollections
-from matplotlib import path as mpath
-from matplotlib import transforms as mtransforms
-import matplotlib.style as mstyle
+from matplotlib import (
+    collections as mcollections, colors as mcolors, patches as mpatches,
+    path as mpath, style as mstyle, transforms as mtransforms)
 
 import sys
 on_win = (sys.platform == 'win32')
@@ -443,3 +440,29 @@ def test_contains_points():
     expected = path.contains_points(points, transform, radius)
     result = ell.contains_points(points)
     assert np.all(result == expected)
+
+
+# Currently fails with pdf/svg, probably because some parts assume a dpi of 72.
+@check_figures_equal(extensions=["png"])
+def test_shadow(fig_test, fig_ref):
+    xy = np.array([.2, .3])
+    dxy = np.array([.1, .2])
+    # We need to work around the nonsensical (dpi-dependent) interpretation of
+    # offsets by the Shadow class...
+    plt.rcParams["savefig.dpi"] = "figure"
+    # Test image.
+    a1 = fig_test.subplots()
+    rect = mpatches.Rectangle(xy=xy, width=.5, height=.5)
+    shadow = mpatches.Shadow(rect, ox=dxy[0], oy=dxy[1])
+    a1.add_patch(rect)
+    a1.add_patch(shadow)
+    # Reference image.
+    a2 = fig_ref.subplots()
+    rect = mpatches.Rectangle(xy=xy, width=.5, height=.5)
+    shadow = mpatches.Rectangle(
+        xy=xy + fig_ref.dpi / 72 * dxy, width=.5, height=.5,
+        fc=np.asarray(mcolors.to_rgb(rect.get_fc())) * .3,
+        ec=np.asarray(mcolors.to_rgb(rect.get_fc())) * .3,
+        alpha=.5)
+    a2.add_patch(shadow)
+    a2.add_patch(rect)