diff --git a/ci/code_checks.sh b/ci/code_checks.sh
index 26c8ae1298630..1f21f48c061e1 100755
--- a/ci/code_checks.sh
+++ b/ci/code_checks.sh
@@ -113,8 +113,6 @@ if [[ -z "$CHECK" || "$CHECK" == "docstrings" ]]; then
         -i "pandas.Index.get_indexer_non_unique PR07,SA01" \
         -i "pandas.Index.get_loc PR07,RT03,SA01" \
         -i "pandas.Index.identical PR01,SA01" \
-        -i "pandas.Index.insert PR07,RT03,SA01" \
-        -i "pandas.Index.intersection PR07,RT03,SA01" \
         -i "pandas.Index.join PR07,RT03,SA01" \
         -i "pandas.Index.names GL08" \
         -i "pandas.Index.nunique RT03" \
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 9acab2642f6be..b6398bc0e9085 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3082,6 +3082,8 @@ def intersection(self, other, sort: bool = False):
         Parameters
         ----------
         other : Index or array-like
+            An Index or an array-like object containing elements to form the
+            intersection with the original Index.
         sort : True, False or None, default False
             Whether to sort the resulting index.
 
@@ -3093,6 +3095,14 @@ def intersection(self, other, sort: bool = False):
         Returns
         -------
         Index
+            Returns a new Index object with elements common to both the original Index
+            and the `other` Index.
+
+        See Also
+        --------
+        Index.union : Form the union of two Index objects.
+        Index.difference : Return a new Index with elements of index not in other.
+        Index.isin : Return a boolean array where the index values are in values.
 
         Examples
         --------
@@ -6624,11 +6634,19 @@ def insert(self, loc: int, item) -> Index:
         Parameters
         ----------
         loc : int
+            The integer location where the new item will be inserted.
         item : object
+            The new item to be inserted into the Index.
 
         Returns
         -------
         Index
+            Returns a new Index object resulting from inserting the specified item at
+            the specified location within the original Index.
+
+        See Also
+        --------
+        Index.append : Append a collection of Indexes together.
 
         Examples
         --------