Question

If each side of a quadrilateral is congruent to its opposite side than the quadrilateral is a parallelogram? True or False

Answer 1

i think True.
By drawing in one of the diagonals, you then get two triangles that you can show to be congruent because their corresponding sides are congruent (SSS theorem). You may then show the angles between the diagonal and each pair of opposite sides of the quadrilateral to be congruent. By extending these sides, you then show that these angles form alternate interior angles for a set of lines. Because the alternate interior angles are congruent, the lines, hence the sides, must be parallel.