Question

select the correct answer from each drop - down menu.
consider parallelogram abcd with center e.
since rotating parallelogram abcd about its center e maps side \\(\overline{cd}\\) onto side \\(\overline{ab}\\) and side \\(\overline{bc}\\) onto side \\(\overline{\quad}\\), opposite sides of parallelograms are \\(\overline{\quad}\\).

Explanation:

Step1: Recall properties of parallelograms and rotations

A parallelogram has rotational symmetry of order 2 about its center. This means rotating the parallelogram by \(180^\circ\) about its center maps each side to its opposite side.

Step2: Determine the rotation angle

For a parallelogram, rotating about its center by \(180^\circ\) (since the order of rotational symmetry is 2, \(360^\circ/2 = 180^\circ\)) maps side \(CD\) to \(AB\) and side \(BC\) to \(AD\) (because opposite sides of a parallelogram are equal and parallel, and rotation by \(180^\circ\) swaps opposite sides). Also, opposite sides of parallelograms are equal (or congruent, and in terms of rotation, the rotation that maps a side to its opposite is \(180^\circ\)).

So the first drop - down (for the angle of rotation) should be \(180^\circ\), the second drop - down (for what \(BC\) maps to) should be \(\overline{AD}\), and the third drop - down (for the property of opposite sides) should be "equal" (or "congruent", but in the context of rotation mapping, the key is the \(180^\circ\) rotation and mapping to opposite sides which are equal).

Answer:

• The angle of rotation: \(180^\circ\)
• The side \(BC\) maps to: \(\overline{AD}\)
• Opposite sides of parallelograms are: equal (or congruent)