diff --git a/.changeset/cyan-seals-yawn.md b/.changeset/cyan-seals-yawn.md
new file mode 100644
index 0000000000..a9e2c75758
--- /dev/null
+++ b/.changeset/cyan-seals-yawn.md
@@ -0,0 +1,5 @@
+---
+"@khanacademy/perseus": minor
+---
+
+Update Polygon graphs to have weighted lines only on keyboard focus
diff --git a/packages/perseus/src/widgets/interactive-graphs/graphs/components/angle-indicators.tsx b/packages/perseus/src/widgets/interactive-graphs/graphs/components/angle-indicators.tsx
index c316dcc72e..6be5d4078f 100644
--- a/packages/perseus/src/widgets/interactive-graphs/graphs/components/angle-indicators.tsx
+++ b/packages/perseus/src/widgets/interactive-graphs/graphs/components/angle-indicators.tsx
@@ -16,7 +16,6 @@ interface PolygonAngleProps {
     centerPoint: vec.Vector2;
     endPoints: [vec.Vector2, vec.Vector2];
     polygonLines: readonly CollinearTuple[];
-    active: boolean;
     range: [Interval, Interval];
     showAngles: boolean;
     snapTo: "grid" | "angles" | "sides";
diff --git a/packages/perseus/src/widgets/interactive-graphs/graphs/polygon.test.tsx b/packages/perseus/src/widgets/interactive-graphs/graphs/polygon.test.tsx
new file mode 100644
index 0000000000..292a6eee20
--- /dev/null
+++ b/packages/perseus/src/widgets/interactive-graphs/graphs/polygon.test.tsx
@@ -0,0 +1,74 @@
+import {render} from "@testing-library/react";
+import {userEvent as userEventLib} from "@testing-library/user-event";
+import {Mafs, Polygon} from "mafs";
+import React from "react";
+
+import {hasFocusVisible} from "./polygon";
+
+import type {UserEvent} from "@testing-library/user-event";
+
+describe("hasFocusVisible", () => {
+    let userEvent: UserEvent;
+    beforeEach(() => {
+        userEvent = userEventLib.setup({
+            advanceTimers: jest.advanceTimersByTime,
+        });
+    });
+
+    it("returns true when polygon is focused", async () => {
+        const ref = React.createRef<SVGPolygonElement>();
+        render(
+            <Mafs width={200} height={200}>
+                <Polygon
+                    points={[
+                        [0, 0],
+                        [0, 2],
+                        [2, 2],
+                        [2, 0],
+                    ]}
+                    svgPolygonProps={{
+                        ref,
+                        tabIndex: 0,
+                    }}
+                />
+            </Mafs>,
+        );
+        const polygon = ref.current;
+        if (polygon) {
+            await userEvent.tab();
+            await userEvent.tab();
+        }
+
+        expect(polygon).toBeInTheDocument();
+        expect(polygon).toHaveFocus();
+        expect(hasFocusVisible(polygon)).toBe(true);
+    });
+
+    it("returns false when polygon is not focused", async () => {
+        const ref = React.createRef<SVGPolygonElement>();
+        render(
+            <Mafs width={200} height={200}>
+                <Polygon
+                    points={[
+                        [0, 0],
+                        [0, 2],
+                        [2, 2],
+                        [2, 0],
+                    ]}
+                    svgPolygonProps={{
+                        ref,
+                        tabIndex: 0,
+                    }}
+                />
+            </Mafs>,
+        );
+        const polygon = ref.current;
+        if (polygon) {
+            await userEvent.tab();
+        }
+
+        expect(polygon).toBeInTheDocument();
+        expect(polygon).not.toHaveFocus();
+        expect(hasFocusVisible(polygon)).toBe(false);
+    });
+});
diff --git a/packages/perseus/src/widgets/interactive-graphs/graphs/polygon.tsx b/packages/perseus/src/widgets/interactive-graphs/graphs/polygon.tsx
index 34d7150942..ab4f65ddfd 100644
--- a/packages/perseus/src/widgets/interactive-graphs/graphs/polygon.tsx
+++ b/packages/perseus/src/widgets/interactive-graphs/graphs/polygon.tsx
@@ -17,8 +17,10 @@ import type {CollinearTuple} from "@khanacademy/perseus";
 type Props = MafsGraphProps<PolygonGraphState>;
 
 export const PolygonGraph = (props: Props) => {
-    const [focused, setFocused] = React.useState(false);
     const [hovered, setHovered] = React.useState(false);
+    // This is more so required for the re-rendering that occurs when state
+    // updates; specifically with regard to line weighting and polygon focus.
+    const [focusVisible, setFocusVisible] = React.useState(false);
 
     const {dispatch} = props;
     const {coords, showAngles, showSides, range, snapStep, snapTo} =
@@ -43,7 +45,6 @@ export const PolygonGraph = (props: Props) => {
             ["angles", "sides"].includes(snapToValue) ? p : snap(snapStep, p),
     });
 
-    const active = hovered || focused || dragging;
     const lastMoveTime = React.useRef<number>(0);
 
     const lines = getLines(points);
@@ -54,7 +55,7 @@ export const PolygonGraph = (props: Props) => {
                 points={[...points]}
                 color="var(--movable-line-stroke-color)"
                 svgPolygonProps={{
-                    strokeWidth: active
+                    strokeWidth: focusVisible
                         ? "var(--movable-line-stroke-weight-active)"
                         : "var(--movable-line-stroke-weight)",
                     style: {fill: "transparent"},
@@ -71,7 +72,6 @@ export const PolygonGraph = (props: Props) => {
                         key={"angle-" + i}
                         centerPoint={point}
                         endPoints={[pt1, pt2]}
-                        active={active}
                         range={range}
                         polygonLines={lines}
                         showAngles={!!showAngles}
@@ -109,10 +109,19 @@ export const PolygonGraph = (props: Props) => {
                         cursor: dragging ? "grabbing" : "grab",
                         fill: hovered ? "var(--mafs-blue)" : "transparent",
                     },
-                    onFocus: () => setFocused(true),
-                    onBlur: () => setFocused(false),
                     onMouseEnter: () => setHovered(true),
                     onMouseLeave: () => setHovered(false),
+                    // Required to remove line weighting when user clicks away
+                    // from the focused polygon
+                    onKeyDownCapture: () => {
+                        setFocusVisible(hasFocusVisible(ref.current));
+                    },
+                    // Required for lines to darken on focus
+                    onFocus: () =>
+                        setFocusVisible(hasFocusVisible(ref.current)),
+                    // Required for line weighting to update on blur. Without this,
+                    // the user has to hover over the shape for it to update
+                    onBlur: () => setFocusVisible(hasFocusVisible(ref.current)),
                     className: "movable-polygon",
                 }}
             />
@@ -143,3 +152,17 @@ function getLines(points: readonly vec.Vector2[]): CollinearTuple[] {
         return [point, next];
     });
 }
+
+export const hasFocusVisible = (
+    element: Element | null | undefined,
+): boolean => {
+    const matches = (selector: string) => element?.matches(selector) ?? false;
+    try {
+        return matches(":focus-visible");
+    } catch (e) {
+        // jsdom doesn't support :focus-visible
+        // (see https://github.com/jsdom/jsdom/issues/3426),
+        // so the call to matches(":focus-visible") will fail in tests.
+        return matches(":focus");
+    }
+};