When reflected across a line of symmetry, a shape having that line of symmetry will fall on itself. These are the actual claims:
(1) The rectangle's diagonals will line up exactly with one another.
(2) A rectangle's diagonals are symmetry lines.
We deduce from the question that the rectangle is mirrored across the symmetry line.
When done, the rectangle's half will fall directly on the other half.
This indicates that the rectangle's diagonal will line up perfectly with the opposite diagonal.
According to the aforementioned claim, a rectangle's diagonal is also its line of symmetry.
To learn more about lines of symmetry and diagonals link is here
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