Math worksheet asking students to fill in the rotational symmetry for various geometric shapes.

Problem Overview:

The task is to determine the rotational symmetry of each given shape. Rotational symmetry refers to the property of a shape that allows it to look identical after being rotated by a certain angle around its center. The goal is to identify the order of rotational symmetry for each shape.

Steps to Solve:

1. Understand Rotational Symmetry:
- A shape has rotational symmetry if it looks the same after being rotated by a certain angle.
- The order of rotational symmetry is the number of times the shape looks the same during a full 360° rotation.

2. Analyze Each Shape:
- For each shape, determine how many times it looks identical as it is rotated through 360°.

3. Calculate the Order:
- The order is calculated as \( \frac{360^\circ}{\text{angle of rotation}} \).

Solution for Each Shape:

#### 1. Triangle (Equilateral Triangle):
- An equilateral triangle looks the same after rotations of 120°, 240°, and 360°.
- Order = \( \frac{360^\circ}{120^\circ} = 3 \).

#### 2. Hexagon (Regular Hexagon):
- A regular hexagon looks the same after rotations of 60°, 120°, 180°, 240°, 300°, and 360°.
- Order = \( \frac{360^\circ}{60^\circ} = 6 \).

#### 3. Trapezoid:
- A general trapezoid does not have rotational symmetry unless it is an isosceles trapezoid with specific properties. Assuming it is a typical trapezoid:
- Order = 1 (it only looks the same at 360° rotation).

#### 4. Rhombus:
- A rhombus looks the same after rotations of 180° and 360°.
- Order = \( \frac{360^\circ}{180^\circ} = 2 \).

#### 5. Right Triangle:
- A right triangle does not have rotational symmetry unless it is an isosceles right triangle. Assuming it is a typical right triangle:
- Order = 1 (it only looks the same at 360° rotation).

#### 6. Circle:
- A circle looks the same at any angle of rotation.
- Order = Infinite (or can be considered as having infinite rotational symmetry).

#### 7. Square:
- A square looks the same after rotations of 90°, 180°, 270°, and 360°.
- Order = \( \frac{360^\circ}{90^\circ} = 4 \).

#### 8. Pentagon (Regular Pentagon):
- A regular pentagon looks the same after rotations of 72°, 144°, 216°, 288°, and 360°.
- Order = \( \frac{360^\circ}{72^\circ} = 5 \).

#### 9. Rectangle:
- A rectangle looks the same after rotations of 180° and 360°.
- Order = \( \frac{360^\circ}{180^\circ} = 2 \).

Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Triangle} & 3 \\
\text{Hexagon} & 6 \\
\text{Trapezoid} & 1 \\
\text{Rhombus} & 2 \\
\text{Right Triangle} & 1 \\
\text{Circle} & \text{Infinite} \\
\text{Square} & 4 \\
\text{Pentagon} & 5 \\
\text{Rectangle} & 2 \\
\end{array}
}
\]