Since the statement does not say that they have exactly two lines of symmetry, I do not believe that there is a counter example.
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NO rectangles are trapezoids
They may have no lines of symmetry or they may have some - it all depends upon the shape of the irregular octagon. Only regular octagons have 8 lines of symmetry.
If your asking what shape has three lines of symmetry, your answer would be an equilateral triangle. You can tell how many lines of symmetry a shape that has all angles of the same measure has by looking at it's angles. Ex., pentagon has five angles--five lines of symmetry; octagon has eight angles, eight lines of symmetry; etc.
Depending on the triangle, there can be 0, 1, or three lines of symmetry. A scalene triangle (all sides of different lengths) will have no lines of symmetry, an isosceles triangle (exactly two sides of the same length) will have one line of symmetry, and an equilateral triangle (all three sides of the same length) will have three lines of symmetry.
First of all to correct your spelling. It is 'parallelogram'. A parallelogram does NOT have any lines of symmetry, unless it is a rectangular paralleligram. Where upon it has two lines of symmetry, viz/ a vertical line through the centre and an horizontal line through the centre.