The parallelogram has rotational symmetry. The parallelogram can merge with itself more than once during a full rotation. The degree of rotation of a parallelogram is $2$: the parallelogram can merge with itself twice during a full rotation.

What is rotational symmetry?

Rotational Symmetry

A shape that has rotational symmetry is a shape that "maps onto itself" and merges with itself, more than once during a full rotation. A shape that manages to merge with itself only after completing a full rotation, is a shape that does not have rotational symmetry.

Center of rotational symmetry:

The point around which the shape rotates.

Rotation level

The number of times the shape manages to merge with itself during a full rotation. Observation - A shape that manages to merge with itself for the first time only after a full rotation is a shape without rotational symmetry.

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Rotational Symmetry

Before talking about rotational symmetry in parallelograms, we are asked What is a shape that has rotational symmetry? A shape that "covers itself" merges with itself, more than once during a complete rotation, is a shape that has rotational symmetry. The center of rotational symmetry is the point around which the shape rotates. The degree of rotation is the number of times the shape manages to merge with itself during a complete rotation. Note - Shapes that manage to merge with themselves only after having completed a full rotation are shapes that do not have rotational symmetry.

In front of us is a parallelogram:

Rotational Symmetry

If we rotate it a quarter turn, it still will not merge with itself. We will see this in the figure:

Rotational Symmetry

Now, let's give it another quarter turn, that is, now a half turn and we will see how it merges with itself, it covers. We will see this in the figure:

Rotational Symmetry

At this point, we can already determine that the parallelogram has rotational symmetry. We have not yet rotated it a full turn and it has already merged with itself. Now we will proceed to a full turn to find out the degree of its rotation.

If we continue rotating another quarter turn, the parallelogram will not cover itself again. We can see this in the figure:

If we keep rotating another quarter turn, that is, now we will have a full turn, the parallelogram will cover itself again, it will merge with itself and this will be the second time. We will see this in the figure:

Therefore, we can determine that the parallelogram has rotational symmetry and its degree of rotation is $2$.

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