Walls and Ceilings - hole in ceiling

i have a 2'x4' hole in my popcorn ceiling from a leak in a pipe in my bathroom above. we fixed the leak but do not know how to patch the popcorn ceiling. do we use drywall but then how do we tape the seam to the popcorn finish? Please help!

Cut the drywall back to the center of a joist. Cut a piece of drywall to fit the hole. Screw down patch. Also screw off the existing drywall. Scrape the texture back about 16" all around the patch. Pre fill any large gaps. Let that dry. Put mesh tape on all seams. Apply Joint compound( I use plus 3) with a ten inch knife on both sides of tape joint. Let dry. Apply a second coat of mud with a twelve inch knife in same fashion. Let dry. Scrape down any high spots. Don't sand. If you need to- feather edges with a sponge. Determine what size texture you have (small, medium, large). Most popular is medium. Buy a bag at home depot, lowes, whatever. Mix with a drill and paddle to a thin mixture. The directions on the bag say let sit for 15 minutes and mix again but the longer the better. Rent a spray rig. Your mix should me the consistancy of pancake batter. Load the texture into the hopper. Spray away. Make sure you spray it on heavy. It will shrink and sometimes wont cover completely. Now if you have it the way you want you could have this problem to address. the color may not match. If thats the case you may consider painting the entire ceiling. Who knows though, it might look good.