To summarize the reflections that carry a parallelogram onto itself, we need to consider the symmetries of a parallelogram, specifically the lines of reflection symmetry.
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Diagonals: A parallelogram has two diagonals. Each diagonal serves as a line of reflection symmetry. Reflecting the parallelogram across either diagonal will result in the same shape as the original parallelogram.
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Midpoints of Opposite Sides: In addition to the diagonals, each pair of opposite sides can also help form lines of reflection. The midpoints of opposite sides of the parallelogram can be connected to create another line of reflection. Reflecting across this line will also carry the shape onto itself.
Thus, the reflections that carry a parallelogram onto itself are:
- Reflection across the line that bisects one diagonal.
- Reflection across the line that bisects the other diagonal.
- Reflection across the line that goes through the midpoints of the opposite sides.
In summary, there are a total of three lines of reflection symmetry in a parallelogram: the two diagonals and the line connecting the midpoints of a pair of opposite sides.