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Which of the following summarizes the reflections that carry a parallelogram onto itself?(1 point)

Responses

A parallelogram has two lines of reflection: flipped on each diagonal will carry it onto itself.
A parallelogram has two lines of reflection: flipped on each diagonal will carry it onto itself.

A parallelogram does not have any lines of reflection.
A parallelogram does not have any lines of reflection.

A parallelogram has two lines of reflection that carry it onto itself: one horizontal through the midpoints of each side, and one vertical through the midpoints of the top and bottom.
A parallelogram has two lines of reflection that carry it onto itself: one horizontal through the midpoints of each side, and one vertical through the midpoints of the top and bottom.

A parallelogram has four lines of symmetry: horizontal through the midpoints, vertical through the midpoints, and both diagonals.

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3 answers

The correct response that summarizes the reflections that carry a parallelogram onto itself is:

A parallelogram has four lines of symmetry: horizontal through the midpoints, vertical through the midpoints, and both diagonals.

This statement accurately reflects the symmetry of a parallelogram, as it indeed has lines of reflection through both diagonals as well as a vertical and horizontal line through the midpoints of the opposite sides.

but parallelograms have no lines of symmetry

I apologize for any confusion in my previous response. To clarify:

A general parallelogram (not specifically a rectangle or rhombus) does not have any lines of symmetry. However, certain types of parallelograms do have line(s) of symmetry:

  1. Rectangles have two lines of symmetry: one vertical and one horizontal.
  2. Rhombuses have two lines of symmetry that are the diagonals.
  3. Squares (which are both rectangles and rhombuses) have four lines of symmetry.

If you are referring to a general parallelogram, it is correct to say that it does not have any lines of symmetry.

So, the correct answer concerning a general parallelogram is indeed that it does not have lines of reflection that carry it onto itself. Thank you for your patience, and I'm here to help if you have any further questions!