Which of the following summarizes the reflections that carry a parallelogram onto itself?

Answer 1

To summarize the reflections that carry a parallelogram onto itself, we need to consider the symmetry operations of the shape. A parallelogram has the following reflections that will map it onto itself:

1. Reflection over the line that bisects the opposite sides: This reflection axis runs vertically or horizontally, depending on the orientation of the parallelogram, and it bisects the angle between the two pairs of opposite sides.

2. Reflection over the diagonal lines: A parallelogram can be reflected over its two diagonals (the lines connecting opposite vertices). Each diagonal serves as a reflection axis, where points on one side of the diagonal are mapped onto corresponding points on the opposite side.

In total, there are four lines of reflection symmetry:

• Two diagonals.
• Two lines bisecting the pairs of opposite sides.

These reflections effectively show the symmetry of the parallelogram because reflecting it across any of these lines will result in the same shape, thus demonstrating its self-symmetry.