diff --git a/common/src/app/common/logic/libraries.cljc b/common/src/app/common/logic/libraries.cljc
index 09683b4445..6468c86bc1 100644
--- a/common/src/app/common/logic/libraries.cljc
+++ b/common/src/app/common/logic/libraries.cljc
@@ -1401,26 +1401,23 @@
                 (dissoc :modifiers))))))))
 
 (defn orient-like
-  "A function that turns each shape of the subtree of `head` around `center`,
-  so that `head` takes the flips and then the rotation of `target`; nil when
-  they already agree."
+  "Turn the subtree of `head` around `center` to match `target`'s matrix.
+   Flip flags can change during a rotation, so they cannot be applied as
+   separate transforms before that rotation."
   [head target center]
-  (let [flip-x? (not= (true? (:flip-x head)) (true? (:flip-x target)))
-        flip-y? (not= (true? (:flip-y head)) (true? (:flip-y target)))
-        flip    (when (or flip-x? flip-y?)
-                  (ctm/resize-modifiers (gpt/point (if flip-x? -1 1) (if flip-y? -1 1)) center))
-        head'   (cond-> head (some? flip) (gsh/transform-shape flip))
-        angle   (- (d/nilv (:rotation target) 0) (d/nilv (:rotation head') 0))
-        rotate? (not (mth/close? (mod angle 360) 0 0.01))
-        angle   (if (> angle 180) (- angle 360) angle)]
-    (when (or (some? flip) rotate?)
-      (fn [shape]
-        (cond-> shape
-          (some? flip)
-          (gsh/transform-shape flip)
-
-          rotate?
-          (as-> shape (gsh/transform-shape shape (ctm/rotation-modifiers shape center angle))))))))
+  (when-not (and (= (:transform head) (:transform target))
+                 (mth/close? (or (:rotation head) 0) (or (:rotation target) 0) 0.01))
+    (let [relative (gmt/multiply (or (:transform target) (gmt/matrix))
+                                 (or (:transform-inverse head) (gmt/matrix)))
+          transform (gmt/transform-in center relative)
+          turned (gsh/apply-transform head transform)
+          angle (- (or (:rotation target) 0) (or (:rotation turned) 0))]
+      (when (or (not (gmt/unit? relative)) (not (mth/close? (mod angle 360) 0 0.01)))
+        (fn [shape]
+          (-> shape
+              (assoc-in [:modifiers :rotation] angle)
+              (gsh/apply-transform transform)
+              (dissoc :modifiers)))))))
 
 (defn- maybe-sync
   [c enabled? done? f]
diff --git a/common/test/common_tests/logic/comp_expected_geometry_test.cljc b/common/test/common_tests/logic/comp_expected_geometry_test.cljc
index 17bb6dac24..9a6f150a5d 100644
--- a/common/test/common_tests/logic/comp_expected_geometry_test.cljc
+++ b/common/test/common_tests/logic/comp_expected_geometry_test.cljc
@@ -11,6 +11,7 @@
    through their constraints (decision (f) of the component contract)."
   (:require
    [app.common.files.changes-builder :as pcb]
+   [app.common.geom.matrix :as gmt]
    [app.common.geom.modifiers :as gm]
    [app.common.geom.shapes :as gsh]
    [app.common.logic.libraries :as cll]
@@ -147,27 +148,29 @@
 
 
 (t/deftest rotating-a-copy-with-text-in-a-detached-child-is-already-synced
-  (let [setup (fn []
-                (tm/make-situation
-                 (-> (thf/sample-file :file1)
-                     (thtx/add-text-component-with-copy [[["Hello world"]]])
-                     (ths/update-shape :main-child :grow-type :auto-height)
-                     (ths/update-shape :copy-child :grow-type :auto-height)
-                     (ths/update-shape :copy-child :touched nil)
-                     (tho/add-simple-component :outer :outer-root :outer-child
-                                               :root-params {:width 100 :height 100})
-                     (thc/instantiate-component :outer :outer-copy))))
-        situation (r/run-variant
-                   {:setup setup
-                    :operation (tm/in-sequence [(n/nest-copy :copy-root :outer-root)
-                                                (n/detach :copy-root)
-                                                (n/rotate :outer-copy 45)])})
-        file (tm/file situation)
-        text (first (filter #(= (thi/id :copy-child) (:shape-ref %))
-                            (vals (:objects (thf/current-page file)))))
-        full (:file (r/sync-cascade file {} (keys (get-in file [:data :components]))))
-        synced (ths/get-shape-by-id full (:id text))]
-    (t/is (some? text))
-    (t/is (gsh/close-attrs? :points (:points text) (:points synced) 0.01))
-    (t/is (mth/close? (:x text) (:x synced) 0.01))
-    (t/is (mth/close? (:y text) (:y synced) 0.01))))
+  (doseq [angle [45 135 225]]
+    (let [setup (fn []
+                  (tm/make-situation
+                   (-> (thf/sample-file :file1)
+                       (thtx/add-text-component-with-copy [[["Hello world"]]])
+                       (ths/update-shape :main-child :grow-type :auto-height)
+                       (ths/update-shape :copy-child :grow-type :auto-height)
+                       (ths/update-shape :copy-child :touched nil)
+                       (tho/add-simple-component :outer :outer-root :outer-child
+                                                 :root-params {:width 100 :height 100})
+                       (thc/instantiate-component :outer :outer-copy))))
+          situation (r/run-variant
+                     {:setup setup
+                      :operation (tm/in-sequence [(n/nest-copy :copy-root :outer-root)
+                                                  (n/detach :copy-root)
+                                                  (n/rotate :outer-copy angle)])})
+          file (tm/file situation)
+          text (first (filter #(= (thi/id :copy-child) (:shape-ref %))
+                              (vals (:objects (thf/current-page file)))))
+          full (:file (r/sync-cascade file {} (keys (get-in file [:data :components]))))
+          synced (ths/get-shape-by-id full (:id text))]
+      (t/is (some? text))
+      (t/is (gmt/close? (:transform text) (:transform synced)))
+      (t/is (gsh/close-attrs? :points (:points text) (:points synced) 0.01))
+      (t/is (mth/close? (:x text) (:x synced) 0.01))
+      (t/is (mth/close? (:y text) (:y synced) 0.01)))))