diff --git a/manim/mobject/mobject.py b/manim/mobject/mobject.py
index 73b1920ff6..40bcd46336 100644
--- a/manim/mobject/mobject.py
+++ b/manim/mobject/mobject.py
@@ -1734,7 +1734,8 @@ def put_start_and_end_on(self, start: Point3D, end: Point3D) -> Self:
         curr_start, curr_end = self.get_start_and_end()
         curr_vect = curr_end - curr_start
         if np.all(curr_vect == 0):
-            raise Exception("Cannot position endpoints of closed loop")
+            self.points = start
+            return self
         target_vect = np.array(end) - np.array(start)
         axis = (
             normalize(np.cross(curr_vect, target_vect))
diff --git a/tests/module/mobject/graphing/test_number_line.py b/tests/module/mobject/graphing/test_number_line.py
index 3fededfab8..56cd7267ed 100644
--- a/tests/module/mobject/graphing/test_number_line.py
+++ b/tests/module/mobject/graphing/test_number_line.py
@@ -2,7 +2,7 @@
 
 import numpy as np
 
-from manim import NumberLine
+from manim import DashedLine, NumberLine
 from manim.mobject.text.numbers import Integer
 
 
@@ -121,3 +121,10 @@ def test_point_to_number():
     np.testing.assert_array_equal(np.round(num_1, 4), np.round(expected, 4))
     np.testing.assert_array_equal(np.round(num_2, 4), np.round(expected, 4))
     np.testing.assert_array_equal(np.round(num_3, 4), np.round(expected, 4))
+
+
+def test_start_and_end_at_same_point():
+    line = DashedLine(np.zeros(3), np.zeros(3))
+    line.put_start_and_end_on(np.zeros(3), np.array([0, 0, 0]))
+
+    np.testing.assert_array_equal(np.round(np.zeros(3), 4), np.round(line.points, 4))