Question

identifying reflectional and rotational symmetry
consider the symmetry of rectangle abcd.
the rectangle has ▼-fold reflectional symmetry.
the rectangle has rotational symmetry of order ▼.
the rectangles rotational symmetry occurs for angles of ▼ degrees.

Explanation:

Step1: Find reflectional symmetry count

A rectangle has 2 lines of reflection: one through the midpoints of opposite long sides, and one through the midpoints of opposite short sides. So it has 2-fold reflectional symmetry.

Step2: Find rotational symmetry order

Rotational symmetry order is the number of times a shape maps to itself in a full 360° rotation. A rectangle maps to itself twice (at 180° and 360°), so order = 2.

Step3: Find rotational symmetry angles

Calculate the angle for each rotation: $\frac{360^\circ}{\text{order}} = \frac{360^\circ}{2} = 180^\circ$. The non-trivial angle where symmetry occurs is 180°.

Answer:

1. 2
2. 2
3. 180