If all you have is a jig saw, there's a slimmer than slim chance in hell that your sides will match up. Circular saw is the way to go unless you have patience enough to go slow enough for the blade to do the work without bending.
If you have a circular saw, it will cut an inch and a half thickness. Skip the clamps and do the following:
Get some finish nails. Do not use ANY other type of nail. FINISH NAILS ONLY. Nail the two pieces together. Cut. Separate. Bingo. Identical pieces. The finish nails will leave a small enough hole that it won't be an issue to fix. Some putty (water putty or wood putty) will fill 'er up, and you'll be good to go. Just don't try to escape filling holes and use only 2 nails

4-6 nails will be good enough, but less than 4 is asking for trouble. If you REALLY want to avoid filling holes, put the nails in the "waste" area of the MDF sheet....you'll still need to stick 2-3 in the "good" area, but that's the easiest way.
Your jig saw will NOT work for this method though.