Not so sure about continuos, but if you meant continuous, the statement is clearly false. It is extremely simple to draw an irregular shape with a continuous line. A ruler may be required for a triangle, square or other polygon, though a good circle will require a huge degree of dexterity.
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None. A line of symmetry, if it exists, is infinitely long and so a third of the line cannot exist as a separate entity.
A symmetrical shape is a mirror image of a shape when a line is drawn through it and some shapes have many lines of symmetry or none at all.
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.
This is either a trick question or a silly question. A rectangle comprises four line and so cannot be drawn with three lines.
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