diff --git a/lucene/core/src/java/org/apache/lucene/geo/Polygon2D.java b/lucene/core/src/java/org/apache/lucene/geo/Polygon2D.java
index c0931b03df3..7db8287f61b 100644
--- a/lucene/core/src/java/org/apache/lucene/geo/Polygon2D.java
+++ b/lucene/core/src/java/org/apache/lucene/geo/Polygon2D.java
@@ -124,13 +124,9 @@ public final class Polygon2D extends EdgeTree {
       }
     }
     if (ax == bx && bx == cx && ay == by && by == cy) {
-      // indexed "triangle" is a point:
-      if (Rectangle.containsPoint(ay, ax, minLat, maxLat, minLon, maxLon) == false) {
-        return Relation.CELL_OUTSIDE_QUERY;
-      }
-      // shortcut by checking contains
+      // indexed "triangle" is a point: shortcut by checking contains
       return contains(ay, ax) ? Relation.CELL_INSIDE_QUERY : Relation.CELL_OUTSIDE_QUERY;
-    } else if (ax == cx && ay == cy) {
+    } else if ((ax == cx && ay == cy) || (bx == cx && by == cy)) {
       // indexed "triangle" is a line segment: shortcut by calling appropriate method
       return relateIndexedLineSegment(ax, ay, bx, by);
     }
diff --git a/lucene/sandbox/src/java/org/apache/lucene/geo/Line2D.java b/lucene/sandbox/src/java/org/apache/lucene/geo/Line2D.java
index 797892e40c5..9f413195b8f 100644
--- a/lucene/sandbox/src/java/org/apache/lucene/geo/Line2D.java
+++ b/lucene/sandbox/src/java/org/apache/lucene/geo/Line2D.java
@@ -57,7 +57,7 @@ public final class Line2D extends EdgeTree {
       if (isPointOnLine(tree, ax, ay)) {
         return Relation.CELL_INSIDE_QUERY;
       }
-    } else if (ax == cx && ay == cy) {
+    } else if ((ax == cx && ay == cy) || (bx == cx && by == cy)) {
       // indexed "triangle" is a line:
       if (tree.crossesLine(ax, ay, bx, by)) {
         return Relation.CELL_CROSSES_QUERY;