Not at all. There are an infinite number of figures that have two lines of symmetry. For a start, an ellipse.
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A quadrilateral cannot have just 3 lines of symmetry. If it has three, then it must have 4 and is a square.
Lines of symmetry must be equal halves.
A parallelogram need have no lines of symmetry.
Yes, a trapezoid may have two lines of symmetry, but the trapezoid must also be a rectangle.If the trapezoid is not also a rectangle, the the most symmetry lines it can have possible is 1 (this can only occur it's an isosceles trapezoid.)
A kite or arrowhead.