Please help
"Is there enough information to prove quadrilateral GHIJ
is a parallelogram?"
Select the answer that is completely correct.

K is the midpoint, so and , and along with the congruent vertical angles ( and ), you would use the SAS (side angle side) congruence theorem to prove the inner pairs of triangles to be congruent.

So, (top and bottom triangles) and (left and right triangles).

Then through CPCTC, we can show the corresponding pieces are congruent leading to and showing the opposite sides of the quadrilateral are congruent. Therefore we do have a parallelogram and enough information to prove it as such.

Side note: CPCTC stands for "corresponding parts of congruent triangles are congruent".

both equations and proportions are better.