With ruler and compasses, we can bisect any given line segment.

If an isosceles triangle has more than one line of symmetry, then it need not be an equilateral triangle.

If a rectangle has more than two lines of symmetry, then it must be a square.

Only one perpendicular bisector can be drawn to a given line segment.

Two perpendiculars can be drawn to a given line from a point not lying on it.