In the figure above, is quadrilateral PQRS a parallelogram?

Is the quadrilateral PQRS a parallelogram where QS is the diagnol.

(1) The area of triangle PQS is equal to the area of triangle QRS.

Well yes: the area of a parallelogram is twice the area of a triangle created by one of its diagonals. But the opposite is not correct: two triangles can share the same base, have the same area BUT their two corresponding side not necessary to be parallel. --> Not sufficient.

(2) QR = RS. --> QRS is isosceles. For PQRS to be parallelogram QPS also must be isosceles, in this case we get rhombus, but it's OK every rhombus is parallelogram. But we don't know that. --> Not sufficient.

(1)+(2) Area QRS=Area PQS, QRS is isosceles. --> PQS can have the same area as QRS and not be isosceles. So not sufficient.

E.

Parallelogram is a quadrilateral with two sets of parallel sides.

The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are equal.

Opposite sides of a parallelogram are equal in length.

Opposite angles of a parallelogram are equal in measure.

The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

The diagonals of a parallelogram bisect each other.

Every rhombus is a parallelogram. Opposite is not correct.

Every square is a parallelogram. Opposite is not correct.