diff --git a/masque/shapes/path.py b/masque/shapes/path.py
index db7831a..b618001 100644
--- a/masque/shapes/path.py
+++ b/masque/shapes/path.py
@@ -314,7 +314,8 @@ class Path(Shape):
         return bounds
 
     def rotate(self, theta: float) -> 'Path':
-        self.vertices = numpy.dot(rotation_matrix_2d(theta), self.vertices.T).T
+        if theta != 0:
+            self.vertices = numpy.dot(rotation_matrix_2d(theta), self.vertices.T).T
         return self
 
     def mirror(self, axis: int) -> 'Path':
diff --git a/masque/shapes/polygon.py b/masque/shapes/polygon.py
index 71c9491..97cc66c 100644
--- a/masque/shapes/polygon.py
+++ b/masque/shapes/polygon.py
@@ -262,7 +262,8 @@ class Polygon(Shape):
                              self.offset + numpy.max(self.vertices, axis=0)))
 
     def rotate(self, theta: float) -> 'Polygon':
-        self.vertices = numpy.dot(rotation_matrix_2d(theta), self.vertices.T).T
+        if theta != 0:
+            self.vertices = numpy.dot(rotation_matrix_2d(theta), self.vertices.T).T
         return self
 
     def mirror(self, axis: int) -> 'Polygon':