Rotational Symmetry Worksheet - Identify the order of rotational symmetry for each of the nine given shapes.

To solve the problem of determining the order of rotational symmetry for each shape, we need to understand what rotational symmetry means. A shape has rotational symmetry if it looks the same after being rotated by a certain angle around its center. The order of rotational symmetry is the number of times the shape looks identical as it completes a full rotation (360°).

Steps to Determine the Order of Rotational Symmetry:

1. Identify the Center of Rotation: This is usually the geometric center of the shape.
2. Rotate the Shape: Mentally or physically rotate the shape in increments until it returns to its original position.
3. Count the Positions: Count how many times the shape looks exactly the same during one full rotation (360°). This count is the order of rotational symmetry.

Analysis of Each Shape:

#### (a) Rectangle
- A rectangle looks the same when rotated by 180° and 360°.
- It does not look the same at 90° or 270°.
- Order of rotational symmetry: 2

#### (b) Square
- A square looks the same when rotated by 90°, 180°, 270°, and 360°.
- Order of rotational symmetry: 4

#### (c) Rhombus
- A rhombus looks the same when rotated by 180° and 360°.
- It does not look the same at 90° or 270°.
- Order of rotational symmetry: 2

#### (d) Star (5-pointed)
- A 5-pointed star looks the same when rotated by 72°, 144°, 216°, 288°, and 360°.
- Order of rotational symmetry: 5

#### (e) Semicircle
- A semicircle only looks the same when rotated by 360°.
- Order of rotational symmetry: 1

#### (f) Parallelogram
- A parallelogram looks the same when rotated by 180° and 360°.
- It does not look the same at 90° or 270°.
- Order of rotational symmetry: 2

#### (g) Trapezoid
- A trapezoid generally does not have rotational symmetry unless it is an isosceles trapezoid with specific properties. For a typical trapezoid, it only looks the same when rotated by 360°.
- Order of rotational symmetry: 1

#### (h) Recycle Symbol
- The recycle symbol looks the same when rotated by 120°, 240°, and 360°.
- Order of rotational symmetry: 3

#### (i) Letter "H"
- The letter "H" looks the same when rotated by 180° and 360°.
- It does not look the same at 90° or 270°.
- Order of rotational symmetry: 2

Final Answer:

\[
\boxed{
\begin{array}{ll}
(a) & 2 \\
(b) & 4 \\
(c) & 2 \\
(d) & 5 \\
(e) & 1 \\
(f) & 2 \\
(g) & 1 \\
(h) & 3 \\
(i) & 2 \\
\end{array}
}
\]