diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index bcaba10d35cd..4025f9a5ebb6 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -159,12 +159,13 @@ def contains_point(self, point, radius=None):
         Parameters
         ----------
         point : (float, float)
-            The point (x, y) to check in target coordinates of
-            ``self.get_transform()``. For patches added to a figure or axes,
-            these are display coordinates.
+            The point (x, y) to check, in target coordinates of
+            ``self.get_transform()``. These are display coordinates for patches
+            that are added to a figure or axes.
         radius : float, optional
-            Adds an additional margin on the patch in coordinates of transform.
-            target. See `.Path.contains_point` for further details.
+            Add an additional margin on the patch in target coordinates of
+            ``self.get_transform()``. See `.Path.contains_point` for further
+            details.
 
         Returns
         -------
@@ -173,9 +174,9 @@ def contains_point(self, point, radius=None):
         Notes
         -----
         The proper use of this method depends on the transform of the patch.
-        Isolated patches do not have a transform. In this, the patch creation
-        coordinates and the point coordinates match. The follow checks that
-        the center of a circle is within the circle
+        Isolated patches do not have a transform. In this case, the patch
+        creation coordinates and the point coordinates match. The following
+        example checks that the center of a circle is within the circle
 
         >>> center = 0, 0
         >>> c = Circle(center, radius=1)
@@ -208,12 +209,13 @@ def contains_points(self, points, radius=None):
         Parameters
         ----------
         points : (N, 2) array
-            The points to check in target coordinates of
-            ``self.get_transform()``. For patches added to a figure or axes,
-            these are display coordinates. Columns contain x and y values.
+            The points to check, in target coordinates of
+            ``self.get_transform()``. These are display coordinates for patches
+            that are added to a figure or axes. Columns contain x and y values.
         radius : float, optional
-            Adds an additional margin on the patch in coordinates of transform.
-            target. See `.Path.contains_points` for further details.
+            Add an additional margin on the patch in target coordinates of
+            ``self.get_transform()``. See `.Path.contains_point` for further
+            details.
 
         Returns
         -------
diff --git a/lib/matplotlib/path.py b/lib/matplotlib/path.py
index 69af3d4c2fbb..b3f18f9eb08c 100644
--- a/lib/matplotlib/path.py
+++ b/lib/matplotlib/path.py
@@ -457,15 +457,15 @@ def contains_point(self, point, transform=None, radius=0.0):
         point : (float, float)
             The point (x, y) to check.
         transform : `matplotlib.transforms.Transform`, optional
-            If not ``None``, *point* will be compared to self transformed
+            If not ``None``, *point* will be compared to ``self`` transformed
             by *transform*; i.e. for a correct check, *transform* should
             transform the path into the coordinate system of *point*.
-        radius : float, default: 0.
-            Adds an additional margin on the path in coordinates of *point*.
+        radius : float, default: 0
+            Add an additional margin on the path in coordinates of *point*.
             The path is extended tangentially by *radius/2*; i.e. if you would
             draw the path with a linewidth of *radius*, all points on the line
             would still be considered to be contained in the area. Conversely,
-            negative values shrink the area; points on the imaginary line
+            negative values shrink the area: Points on the imaginary line
             will be considered outside the area.
 
         Returns
@@ -492,15 +492,15 @@ def contains_points(self, points, transform=None, radius=0.0):
         points : (N, 2) array
             The points to check. Columns contain x and y values.
         transform : `matplotlib.transforms.Transform`, optional
-            If not ``None``, *points* will be compared to self transformed
+            If not ``None``, *points* will be compared to ``self`` transformed
             by *transform*; i.e. for a correct check, *transform* should
             transform the path into the coordinate system of *points*.
         radius : float, default: 0.
-            Adds an additional margin on the path in coordinates of *points*.
+            Add an additional margin on the path in coordinates of *points*.
             The path is extended tangentially by *radius/2*; i.e. if you would
             draw the path with a linewidth of *radius*, all points on the line
             would still be considered to be contained in the area. Conversely,
-            negative values shrink the area; points on the imaginary line
+            negative values shrink the area: Points on the imaginary line
             will be considered outside the area.
 
         Returns