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a rectangle has 2 lines of symmetry: one runs from the center of one of the shorter sides to the center of the other short side. The second runs from the center of one of the longer sides to the center of the other longer side. Diagonals are not lines of symmetry.

Many textbooks use what is called the folding test to find lines of symmetry of plane shapes. This tests says that when the folded part sits perfectly on top so that all the edges are matching, then the fold line is a line of symmetry. If we use this definition, then a diagonal is not a line of symmetry of a rectangle. We would find 2 lines of symmetry using this definition.

Many books define both reflective and rotational symmetries. In fact, in more advanced algebra we look at groups that deal with this. Here is some interesting info about how that would would work with a rectangle. First you would need to identify the corners of the rectangle by using numbers or letters such as ABCD.

Using this we can see two rotational symmetries and two reflective or line symmetries of the rectangle. Now think of symmetries as a function mapping the points of the rectangle back on themselves. Using this idea we can define the product of these functions or transformations. This would be one symmetry followed by another. A composition of symmetries.

A rectangle has two lines of symmetry, each of which is a perpendicular bisector to two opposite sides of the rectangle.
A rectangle has two lines of symmetry

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