diff --git a/lib/web_ui/lib/src/engine/html/path/path_ref.dart b/lib/web_ui/lib/src/engine/html/path/path_ref.dart
index 1cbc082a836a4..7e66e42ee87db 100644
--- a/lib/web_ui/lib/src/engine/html/path/path_ref.dart
+++ b/lib/web_ui/lib/src/engine/html/path/path_ref.dart
@@ -263,15 +263,12 @@ class PathRef {
         // The location delta of control point specifies corner radius.
         if (vector1_0x != 0.0) {
           // For CW : Top right or bottom left corners.
-          assert(vector2_1x == 0.0 && vector1_0y == 0.0);
           dx = vector1_0x.abs();
           dy = vector2_1y.abs();
         } else if (vector1_0y != 0.0) {
-          assert(vector2_1x == 0.0 || vector2_1y == 0.0);
           dx = vector2_1x.abs();
           dy = vector1_0y.abs();
         } else {
-          assert(vector2_1y == 0.0);
           dx = vector1_0x.abs();
           dy = vector1_0y.abs();
         }
@@ -288,9 +285,19 @@ class PathRef {
         radii.add(ui.Radius.elliptical(dx, dy));
         ++cornerIndex;
       } else {
-        assert((verb == SPath.kLineVerb &&
-                ((pts[2] - pts[0]) == 0 || (pts[3] - pts[1]) == 0)) ||
-            verb == SPath.kCloseVerb);
+        if (assertionsEnabled) {
+          if (verb == SPath.kLineVerb) {
+            final bool isVerticalOrHorizontal =
+              SPath.nearlyEqual(pts[2], pts[0]) ||
+              SPath.nearlyEqual(pts[3], pts[1]);
+            assert(
+              isVerticalOrHorizontal,
+              'An RRect path must only contain vertical and horizontal lines.'
+            );
+          } else {
+            assert(verb == SPath.kCloseVerb);
+          }
+        }
       }
     }
     return ui.RRect.fromRectAndCorners(bounds,
diff --git a/lib/web_ui/test/html/path_ref_test.dart b/lib/web_ui/test/html/path_ref_test.dart
new file mode 100644
index 0000000000000..2eaff94dfeab7
--- /dev/null
+++ b/lib/web_ui/test/html/path_ref_test.dart
@@ -0,0 +1,78 @@
+// Copyright 2013 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+import 'package:test/bootstrap/browser.dart';
+import 'package:test/test.dart';
+import 'package:ui/src/engine.dart';
+import 'package:ui/ui.dart';
+
+// TODO(yjbanov): https://github.com/flutter/flutter/issues/76885
+const bool issue76885Exists = true;
+
+void main() {
+  internalBootstrapBrowserTest(() => testMain);
+}
+
+void testMain() {
+  test('PathRef.getRRect with radius', () {
+    final SurfacePath path = SurfacePath();
+    final RRect rrect = RRect.fromLTRBR(0, 0, 10, 10, const Radius.circular(2));
+    path.addRRect(rrect);
+    expect(path.toRoundedRect(), rrect);
+  });
+
+  test('PathRef.getRRect with radius larger than rect', () {
+    final SurfacePath path = SurfacePath();
+    final RRect rrect = RRect.fromLTRBR(0, 0, 10, 10, const Radius.circular(20));
+    path.addRRect(rrect);
+    expect(
+      path.toRoundedRect(),
+      // Path.addRRect will correct the radius to fit the dimensions, so when
+      // extracting the rrect out of the path we don't get the original.
+      RRect.fromLTRBR(0, 0, 10, 10, const Radius.circular(5)),
+    );
+  });
+
+  test('PathRef.getRRect with zero radius', () {
+    final SurfacePath path = SurfacePath();
+    final RRect rrect = RRect.fromLTRBR(0, 0, 10, 10, const Radius.circular(0));
+    path.addRRect(rrect);
+    expect(path.toRoundedRect(), isNull);
+    expect(path.toRect(), rrect.outerRect);
+  });
+
+  test('PathRef.getRRect elliptical', () {
+    final SurfacePath path = SurfacePath();
+    final RRect rrect = RRect.fromLTRBR(0, 0, 10, 10, const Radius.elliptical(2, 4));
+    path.addRRect(rrect);
+    expect(path.toRoundedRect(), rrect);
+  });
+
+  test('PathRef.getRRect elliptical zero x', () {
+    final SurfacePath path = SurfacePath();
+    final RRect rrect = RRect.fromLTRBR(0, 0, 10, 10, const Radius.elliptical(0, 3));
+    path.addRRect(rrect);
+    expect(path.toRoundedRect(), isNull);
+    expect(path.toRect(), rrect.outerRect);
+  });
+
+  test('PathRef.getRRect elliptical zero y', () {
+    final SurfacePath path = SurfacePath();
+    final RRect rrect = RRect.fromLTRBR(0, 0, 10, 10, const Radius.elliptical(3, 0));
+    path.addRRect(rrect);
+    expect(path.toRoundedRect(), isNull);
+    expect(path.toRect(), rrect.outerRect);
+  });
+
+  // This test demonstrates the issue with attempting to reconstruct an RRect
+  // with imprecision introduced by comparing double values. We should fix this
+  // by removing the need to reconstruct rrects:
+  // https://github.com/flutter/flutter/issues/76885
+  test('PathRef.getRRect with nearly zero corner', () {
+    final SurfacePath path = SurfacePath();
+    final RRect original = RRect.fromLTRBR(0, 0, 10, 10, const Radius.elliptical(0.00000001, 5));
+    path.addRRect(original);
+    expect(path.toRoundedRect(), original);
+  }, skip: issue76885Exists);
+}