Answer :
The complete statement is: Since rotating parallelogram ABCD about its center E maps side CD onto side AB and side BC onto side DA, opposite sides of parallelograms are congruent.
The correct answer is: opposite sides of parallelograms are congruent
Since rotating parallelogram ABCD about its center E maps side CD onto side AB and side BC onto side DA, this means that the opposite sides of the parallelogram are congruent.
In other words, side CD is congruent to side AB, and side BC is congruent to side DA.
Therefore, the complete statement is:
Since rotating parallelogram ABCD about its center E maps side CD onto side AB and side BC onto side DA, opposite sides of parallelograms are congruent.
Final answer:
In a parallelogram, opposite sides are equal and parallel. Upon rotation around its center, the sides of the parallelogram map onto each other due to their congruence and symmetrical positioning around the center. This identifies a parallelogram as a symmetrical shape in geometry.
Explanation:
The subject under discussion here is the behaviour of a parallelogram under rotation. In a parallelogram, the opposite sides are equal and parallel. When a parallelogram is rotated around its center, the sides map onto each other because they are congruent (same length) and positioned symmetrically about the center of the parallelogram.
For example, in your parallelogram ABCD, when you rotate it about the center point E, side CD ends up in the position where side AB was because it is equally distant from E but in the opposite direction. Similarly, side BC becomes side AD after rotation around E.
This property of mapping onto each other upon rotation also demonstrates that a parallelogram is a type of 'symmetrical shape' in geometry, which means it can be mapped onto itself by some rotation, reflection, or translation.
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