Question

a quadrilateral has four congruent sides. must the quadrilateral be a parallelogram? justify your answer.
yes; because opposite sides are congruent, the parallelogram opposite sides converse applies.
yes; because four sides are congruent, the quadrilateral is a square, which is a parallelogram.
no; the quadrilateral could be a rhombus, rectangle, or square, so you cannot tell whether it is a parallelogram.
no; a quadrilateral with four congruent sides may not have opposite sides parallel.

Explanation:

A quadrilateral with four congruent sides does not guarantee opposite sides are parallel. A concave quadrilateral called a dart has four congruent sides but is not a parallelogram, as its opposite sides are not parallel. The first two options are incorrect because they assume all such quadrilaterals are parallelograms, and the third option is wrong because rhombuses and squares are parallelograms, and rectangles do not have four congruent sides.

Answer:

no; A quadrilateral with four congruent sides may not have opposite sides parallel.