Problem Explanation:
The task involves understanding
rotational symmetry and determining whether a given shape has rotational symmetry. A shape has rotational symmetry if, after being rotated by a certain angle, it matches its original appearance.
#### Key Concepts:
1.
Rotational Symmetry: A shape has rotational symmetry if it looks the same after being rotated by a specific angle.
2.
Order of Symmetry: The number of times a shape matches itself during a full rotation (360°).
3.
Angle of Rotation: The smallest angle by which the shape can be rotated to match itself.
#### Provided Examples:
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Example 1: A cross-shaped figure is shown. It is rotated by 90° and matches its original appearance.
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Example 2: An arrow-shaped figure is shown. It is rotated by 90° and does not match its original appearance.
Solution:
#### Step 1: Analyze the Cross-Shaped Figure
- The cross-shaped figure is rotated by 90°.
- After a 90° rotation, the figure looks exactly the same as the original.
- This indicates that the cross-shaped figure has rotational symmetry.
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Reasoning: The cross shape can be rotated by 90°, 180°, 270°, and 360°, and it will always look the same. Therefore, it has rotational symmetry of order 4.
#### Step 2: Analyze the Arrow-Shaped Figure
- The arrow-shaped figure is rotated by 90°.
- After a 90° rotation, the figure does not look the same as the original.
- The orientation of the arrow changes, and it no longer matches the original shape.
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Reasoning: The arrow shape does not have any angle of rotation (other than 360°) where it matches its original appearance. Therefore, it does not have rotational symmetry.
Final Answer:
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Cross-Shaped Figure: Has rotational symmetry.
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Arrow-Shaped Figure: Does not have rotational symmetry.
$$
\boxed{\text{The cross-shaped figure has rotational symmetry, while the arrow-shaped figure does not.}}
$$
Parent Tip: Review the logic above to help your child master the concept of line and rotational symmetry worksheet.
