Proving the opposite sides are parallel is the correct first step. If the quadrilateral is not a parallelogram, it cannot be a rhombus.
After knowing the quadrilateral is a parallelogram, we must know whether the sides are congruent. To do this, we must use the distance formula to find the length of each side.
Opposite sides being parallel proves that hte figure is a parallelogram. The sides only appear to be equal so his conclusion is not valid. He would need to show that 2 adjacent sides of the parallelogram are equal ( using the distance formula) to prove that it is a rhombus.
