MatthewMansfield:
It is a simple truss, and usually we think in terms of the joints being pinned. If that is true there can be no vert. reaction transmitted to “D”, because there is no moment at the joint to the right of “D”. If on the other hand, the truss had fixed joints (not pinned, but continuous at the joints, or maybe just the bot. chord was continuous), then some vert. reaction would be transmitted to “D”.

Edit: But, it is an unstable truss if all the joints are pinned, unless you install a diagonal from the lower chord mid length joint up to the upper right top chord corner joint. Then, the parallelogram can not change shape.

In order to get the reactions shown, member from D to the connection of the diagonal must be pinned at the connection of the diagonal, but as dhengr said, at least one of the four corners of the parallelogram must be fixed, or the parallelogram collapses, and the 2 sides between A and G become one straight section. Without knowing which of the corners are fixed, the forces in the members of the parallelogram cannot be determined.

Rod Smith, P.E., The artist formerly known as HotRod10