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It all depends what types of shapes, but take for example a circle, it can have multiple lines of symmetry.
You would call the group of shapes which has at least one line of symmetry symmetrical shapes. Stars, circles, and rectangles are considered symmetrical shapes.
A line is a series of points extending infinitely in opposite directions. Because a single point has no dimension we get only one dimension when we line the points up.
Yes. A line segment has one dimension. There are lots of one-dimension shapes. like a ray, line segment and line.
A line is one dimensional. All two dimensional shapes have height and width.