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A line segment that divides a circle in two is a chord.If the two parts of the circle are equal, the line segment is a diameter.See 'The Parts of the Circle' in Sources and related links, below.
Every line bisector divides a line into two halves: by definition!
A cord that crosses the center of a circle is a diameter, which divides the circle into two equal halves. It is a line segment, and it is the longest cord that can be drawn within a circle.However, if the segment begins at the center rather than crosses through it, and has the other endpoint on the circumference of the circle, it is not a cord, but is a radius of that circle.
If you take a circle for example, a line of symmetry is any line that can go through that circle and if you fold the circle in half it will be equal. So a line of symmetry is a line that you divide any shape in half with and have both halves be the same.