Why does a circle have many lines of symmetry??
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the perimeter of the circle is continuous, a diameter can be drawn from an uncountably many number of places starting from a point on the perimeter. For that reason, there are not only an infinite number of lines, there are an uncountably infinite number of lines of symmetry.
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Since there are an infinite number of lines through the centre, the circle has an infinite number of lines of symmetry. When the circle is folded over a line of symmetry, the parts of the circle on each side of the line match up. This means that the parts of the circle on each side of the line must have the same area.
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