Answer:
(In order of the boxes)
BJ
CK
HJ
HK
JK
Explanation:
Sorry I didn't get to this sooner ;)
First off, we can see that BJ is parallel to AH, and is the same length. That goes into our first box. Next is the second box. This is one is more tricky, as the lines are not right across from each other, but it is CK.
For the 3rd box, we can see that there is only *one* line segment that is parallel to AB, and that would be HJ.
For the 4th box, the only line that is parallel would be HK (just from looking)
And the final box is a tad bit more difficult. If we look up around AH, no lines are parallel to BC there. Let's look at JK. It certainly appears parallel, so it must be.