TanZen is a classic tangram game. It is so well done, that you can just lose yourself in the solving. It works smoothly and the controls are very intuitive. Just slide the pieces in place. Tap to flip, spin to rotate. There is even some soothing background music if you care to enjoy that, too.
I have had the TanZen game on my iPhone since the day I got my first iPhone. (The iPad hadn’t been invented yet. Obviously I’ve had this game for a long time, and it has never crashed or given me grief in any way.)
There are several versions of the game available. One for the iPhone, and another HD version for the iPad. In both cases there is a free version (I’ll provide links to the free ones). If you enjoy it, and want more puzzles, you always have the option to buy more.
But the free versions give you close to 50 puzzles, so you can thoroughly enjoy TanZen without laying out any $$$$$$.