No, a rhombus is a quadrilateral, with four equal-length sides and opposite sides parallel to each other. All rhombuses are parallelograms, but not all parallelograms are rhombuses. The opposite interior angles of rhombuses are always congruent. A parallelogram is just a four sided closed shape where opposite sides are parallel.
The two triangles are congruent because every corresponding side has the same length, & every corresponding angle has the same measure. In short she's correct
