Grade 4 Geometry worksheet on identifying rotational symmetry with various shapes.

Let's solve the problem step by step.

Task:

Identify which shapes have rotational symmetry.
Rotational symmetry means that a shape looks the same after being rotated by a certain angle (less than 360°) around its center.

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Step-by-step Analysis of Each Shape:

1. Top-left (Orange shape):
- This is a cross-like shape with four arms.
- It looks the same when rotated by 90°, 180°, 270°, and 360°.
- ✔ Has rotational symmetry (order 4).

2. Top-right (Blue octagon):
- A regular octagon has 8 equal sides and angles.
- It looks the same every 45° (360° ÷ 8).
- ✔ Has rotational symmetry (order 8).

3. Middle-left (Green hexagon):
- A regular hexagon has 6 equal sides.
- Looks the same every 60° (360° ÷ 6).
- ✔ Has rotational symmetry (order 6).

4. Middle-right (Red triangle):
- This is an isosceles triangle, not equilateral.
- It does not look the same unless rotated 360°.
- ✘ No rotational symmetry.

5. Bottom-left (Purple arrow shape):
- This is a symmetric arrow pointing up.
- If you rotate it 180°, it becomes upside down — doesn't match.
- Only looks the same at 360°.
- ✘ No rotational symmetry.

6. Bottom-middle (Orange double-arrow):
- Two arrows pointing left and right.
- If rotated 180°, it still looks the same (the arrows swap places but the overall shape matches).
- ✔ Has rotational symmetry (order 2).

7. Bottom-left (Gray rectangle with circle):
- The rectangle has a circle in the middle.
- Rotating 180° will keep the shape looking the same because:
- Rectangle is symmetric.
- Circle is symmetric.
- ✔ Has rotational symmetry (order 2).

8. Bottom-right (Blue lightning bolt):
- Irregular shape.
- No rotation less than 360° makes it look the same.
- ✘ No rotational symmetry.

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✔ Final Answer: Check the boxes for the following shapes:

- Orange cross (top-left)
- Blue octagon (top-right)
- Green hexagon (middle-left)
- Orange double-arrow (bottom-middle)
- Gray rectangle with circle (bottom-left)

> ✘ Do not check:
> - Red triangle
> - Purple arrow
> - Blue lightning bolt

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✔ Shapes with Rotational Symmetry:

- Top-left (orange cross)
- Top-right (blue octagon)
- Middle-left (green hexagon)
- Bottom-middle (orange double-arrow)
- Bottom-left (gray rectangle with circle)

✔ Check these five boxes.