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Which transformation will always map a parallelogram onto itself?

a 90° rotation about its center

a reflection across one of its diagonals

a 180° rotation about its center

a reflection across a line joining the midpoints of opposite sides

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taskmasters
"A 180° rotation about its center" is the one transformation among the following choices given in the question that will always map a parallelogram onto itself. The correct option among all the options that are given in the question is the third option or the penultimate option. I hope it helps you.
JeanaShupp

Answer: a 180° rotation about its center


Step-by-step explanation:

A parallelogram has rotational symmetry of order 2.

Thus, rotation transformation maps a parallelogram onto itself 2 times during a rotation of [tex]360^{\circ}[/tex] about its center.

And that is at [tex]180^{\circ}[/tex] and [tex]360^{\circ}[/tex] about its center.

Therefore, a 180° rotation about its center will always map a parallelogram onto itself .

  1. A figure has rotational symmetry when it can be rotated and it still appears exactly the same.
  2. The order of rotational symmetry of a shape is the number of times it can be rotated around [tex]360^{\circ}[/tex] and still appear the same.

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