Question

select the correct answer from each drop - down menu. a square rotated about its center by 360° maps onto itself at different angles of rotation. a square can be reflected onto itself across different lines of reflection.

Explanation:

Step1: Analyze rotation symmetry of square

A square has rotational symmetry. The order of rotational symmetry of a square is \(4\). The angles of rotation for which a square maps onto itself are \(\frac{360^{\circ}}{4} = 90^{\circ}\), \(2\times90^{\circ}=180^{\circ}\), \(3\times90^{\circ} = 270^{\circ}\), and \(360^{\circ}\). So there are \(4\) different angles of rotation (\(90^{\circ},180^{\circ},270^{\circ},360^{\circ}\)) about its center by which a square maps onto itself.

Step2: Analyze reflection symmetry of square

A square has \(4\) lines of reflection. Two lines are the diagonals of the square, and two lines are the lines joining the mid - points of opposite sides.

Answer:

The first blank: \(4\); The second blank: \(4\)