-- A parallelogram is always a quadrilateral. -- A quadrilateral is sometimes a parallelogram.
Always
never
Unfortunately, there is no such thing as a parallelogaram. However, I'm sure you were refering to the shape known as a parallelogram. A parallelogram is a quadrilateral with two sets of parallel sides. Parallel, by the way, means two lines going in the exact same direction that will never cross. Keep in mind that, for example, a square can be a parallelogram while still being a square and a rectangle can be a parallelogram while still being a a rectangle.
A quadrilateral. Could be a rhombus, trapezium, kite, parallelogram with no right angles. Never a square or rectangle.
Always. In fact, one method of proving a quadrilateral a rhombus is by first proving it a parallelogram, and then proving two consecutive sides congruent, diagonals bisecting verticies, etc.
First of all, a trapezoid is not always a parallelogram. Did you mean the reverse: "Why is a parallelogram also a trapezoid"? If so, this depends upon your definition of a trapezoid and parallelogram. Some people define a trapezoid as a quadrilateral with exactly one pair of parallel sides, and a parallelogram as a quadrilateral with exactly two pairs of parallel sides. According to these definitions, a trapezoid can *NEVER* be a parallelogram, so your question is meaningless. However, others might define a trapezoid as a quadrilateral with one *or two* pairs of parallel sides. If you use this definition, then all parallelograms are also trapezoids, much in the same manner that all squares are also rectangles.
a parallelogram will never ever be a rhombus
There is no quadrilateralthat has 1 line of symmetry as quadrilaterals have to have at least 1 line of symmetry.
A parallelogram can meet
A rhombus is a special kind of parallelogram: one in which all sides are equal. It is not true to say that a parallelogram is never a rhombus.
Answer: No, never. Answer: A quadrilateral has four sides. A triangle has three sides.