Can any shape have rotational symmetry of order greater than $2$ without having lines of symmetry?

Draw the figure obtained on rotating the following parallelogram clockwise by half of a complete turn. Would the figure obtained be any different if it was rotated anticlockwise by half of a complete turn? Give reason for your answer.

Draw the figure obtained on rotating the following triangle by half-of a complete turn.

Find the order of rotational symmetry of the following equilateral triangle by drawing its different positions on rotation by one-third of a complete turn.

Find the number of lines of symmetry and the order of rotational symmetry of the following figure.

Find the number of lines of symmetry and the order of rotational symmetry of the following figure.

Draw all the lines of symmetry in the pattern.

Draw all the lines of symmetry in each pattern.