Question

determine whether each object has reflectional symmetry and whether it has rotational symmetry. draw all lines of reflectional symmetry, and write angles of rotation (up to 180°) that map the figure into itself. 10. 11. 12.

Explanation:

Step1: Analyze figure 10

The cross - like figure has 4 lines of reflectional symmetry (vertical, horizontal and two diagonal lines). It has rotational symmetry. The angles of rotation that map it onto itself are 90°, 180°, 270°.

Step2: Analyze figure 11

The infinity symbol has 2 lines of reflectional symmetry (vertical and horizontal). It has rotational symmetry. The angles of rotation that map it onto itself are 180°.

Step3: Analyze figure 12

The anchor figure has 1 line of reflectional symmetry (a vertical line through the center). It has no rotational symmetry (except 360° which is not counted for non - trivial cases up to 180°).

Answer:

1. Lines of reflectional symmetry: 4 (vertical, horizontal, two diagonal). Angles of rotation: 90°, 180°, 270°.
2. Lines of reflectional symmetry: 2 (vertical, horizontal). Angles of rotation: 180°.
3. Lines of reflectional symmetry: 1 (vertical). Angles of rotation: None (up to 180°).