diff --git a/django/contrib/gis/geos/coordseq.py b/django/contrib/gis/geos/coordseq.py
index 15400e08fe..da940e75f8 100644
--- a/django/contrib/gis/geos/coordseq.py
+++ b/django/contrib/gis/geos/coordseq.py
@@ -70,12 +70,12 @@ class GEOSCoordSeq(GEOSBase):
     def _checkindex(self, index):
         "Check the given index."
         if not (0 <= index < self.size):
-            raise IndexError("invalid GEOS Geometry index: %s" % index)
+            raise IndexError("Invalid GEOS Geometry index: %s" % index)
 
     def _checkdim(self, dim):
         "Check the given dimension."
         if dim < 0 or dim > 2:
-            raise GEOSException('invalid ordinate dimension "%d"' % dim)
+            raise GEOSException('Invalid ordinate dimension: "%d"' % dim)
 
     def _get_x(self, index):
         return capi.cs_getx(self.ptr, index, byref(c_double()))
diff --git a/django/contrib/gis/geos/geometry.py b/django/contrib/gis/geos/geometry.py
index 8bbe2c264a..870a615e4f 100644
--- a/django/contrib/gis/geos/geometry.py
+++ b/django/contrib/gis/geos/geometry.py
@@ -346,7 +346,7 @@ class GEOSGeometryBase(GEOSBase):
         two Geometries match the elements in pattern.
         """
         if not isinstance(pattern, str) or len(pattern) > 9:
-            raise GEOSException("invalid intersection matrix pattern")
+            raise GEOSException("Invalid intersection matrix pattern.")
         return capi.geos_relatepattern(self.ptr, other.ptr, force_bytes(pattern))
 
     def touches(self, other):
@@ -499,7 +499,9 @@ class GEOSGeometryBase(GEOSBase):
             # source SRS.
             srid = None
         elif srid is None or srid < 0:
-            raise GEOSException("Calling transform() with no SRID set is not supported")
+            raise GEOSException(
+                "Calling transform() with no SRID set is not supported."
+            )
 
         # Creating an OGR Geometry, which is then transformed.
         g = gdal.OGRGeometry(self._ogr_ptr(), srid)
diff --git a/django/contrib/gis/geos/polygon.py b/django/contrib/gis/geos/polygon.py
index 6f76b57005..9e8d30647b 100644
--- a/django/contrib/gis/geos/polygon.py
+++ b/django/contrib/gis/geos/polygon.py
@@ -103,7 +103,7 @@ class Polygon(GEOSGeometry):
         param,
         msg=(
             "Parameter must be a sequence of LinearRings or objects that can "
-            "initialize to LinearRings"
+            "initialize to LinearRings."
         ),
     ):
         "Try to construct a ring from the given parameter."
diff --git a/tests/gis_tests/geos_tests/test_coordseq.py b/tests/gis_tests/geos_tests/test_coordseq.py
index 507a22d1a0..6888c34824 100644
--- a/tests/gis_tests/geos_tests/test_coordseq.py
+++ b/tests/gis_tests/geos_tests/test_coordseq.py
@@ -9,7 +9,7 @@ class GEOSCoordSeqTest(SimpleTestCase):
             with self.subTest(i):
                 self.assertEqual(coord_seq[i], (i, i))
         for i in (-3, 10):
-            msg = "invalid GEOS Geometry index: %s" % i
+            msg = "Invalid GEOS Geometry index: %s" % i
             with self.subTest(i):
                 with self.assertRaisesMessage(IndexError, msg):
                     coord_seq[i]
diff --git a/tests/gis_tests/geos_tests/test_geos.py b/tests/gis_tests/geos_tests/test_geos.py
index b07c7c04b7..33b58df5f0 100644
--- a/tests/gis_tests/geos_tests/test_geos.py
+++ b/tests/gis_tests/geos_tests/test_geos.py
@@ -651,7 +651,7 @@ class GEOSTest(SimpleTestCase, TestDataMixin):
                 # Testing polygon construction.
                 msg = (
                     "Parameter must be a sequence of LinearRings or "
-                    "objects that can initialize to LinearRings"
+                    "objects that can initialize to LinearRings."
                 )
                 with self.assertRaisesMessage(TypeError, msg):
                     Polygon(0, [1, 2, 3])
@@ -776,7 +776,7 @@ class GEOSTest(SimpleTestCase, TestDataMixin):
     def test_relate_pattern(self):
         "Testing relate() and relate_pattern()."
         g = fromstr("POINT (0 0)")
-        msg = "invalid intersection matrix pattern"
+        msg = "Invalid intersection matrix pattern."
         with self.assertRaisesMessage(GEOSException, msg):
             g.relate_pattern(0, "invalid pattern, yo")
         for rg in self.geometries.relate_geoms:
@@ -1078,7 +1078,7 @@ class GEOSTest(SimpleTestCase, TestDataMixin):
                 # Should only be able to use __setitem__ with LinearRing geometries.
                 msg = (
                     "Parameter must be a sequence of LinearRings or "
-                    "objects that can initialize to LinearRings"
+                    "objects that can initialize to LinearRings."
                 )
 
                 with self.assertRaisesMessage(TypeError, msg):
@@ -1309,7 +1309,7 @@ class GEOSTest(SimpleTestCase, TestDataMixin):
                 if isinstance(g, Point):
                     # IndexError is not raised in GEOS 3.8.0.
                     if geos_version_tuple() != (3, 8, 0):
-                        msg = "invalid GEOS Geometry index:"
+                        msg = "Invalid GEOS Geometry index:"
                         with self.assertRaisesMessage(IndexError, msg):
                             g.x
                 elif isinstance(g, Polygon):
@@ -1443,7 +1443,7 @@ class GEOSTest(SimpleTestCase, TestDataMixin):
         """Testing `transform` method (no SRID or negative SRID)"""
 
         g = GEOSGeometry("POINT (-104.609 38.255)", srid=None)
-        msg = "Calling transform() with no SRID set is not supported"
+        msg = "Calling transform() with no SRID set is not supported."
         with self.assertRaisesMessage(GEOSException, msg):
             g.transform(2774)