1. Parallelogram Rectangle* Rhombus Square*
*Without knowing there are right angles for the interior angles, you really shouldn't claim these figures are a rectangle or square.

2. J K L M
While squares, rectangles and rhombuses all have this in common. Without more information the only thing we can classify JKLM is as a parallelogram.

3. parallelogram
rhombus
Squares
square

4. trapezoid
supplementary
FG HJ
parallel
trapezoid
isosceles
base angles
isosceles trapezoid

5. QRST is a kite since it has two pairs of congruent consecutive sides but the opposite sides aren't congruent or parallel.
Yes, there is enough information to say BCDE is a rectangle. There are 3 right angles given, so the 4th angle must be right also. Since the opposite sides are congruent it is a parallelogram. A parallelogram with 4 right angles is a rectangle by definition.