Endgames are fun?!

In preparation for the Minnesota Closed tournament, I am studying the Class A and Expert sections of Silman's Complete Endgame Course.

If I had understood them earlier, I might have saved a draw in this position from my loss in the Minnesota Open:

1.Kd6? is what I played here. The problem with this move, is that Black will be able to fence off the White king, after 1...Rf5 2.Rxc4 Rxh5 and his king can "hide" in the shadow of White's king to defend the pawn, so the Black rook will be able to come out and get into a better position.

What I need to work towards, is a K vs K+rook pawn ending with my king close enough to reach g1, or a K+R vs K+R+rook pawn with my rook behind the pawn on the h-file.

The move is 1.Kb5. Even though White is moving his king away from the h-file, White will get one of the two endings he wants. 1...Rf5 2.Rxe5 Kxe5 3.Kxc4 Kg4 and White's king gets to g1 and a draw.

Dead Draw

If Black tries to preserve his rook to fence off the White king 1...c3 2.Rxc3 Rf5+ 3.Kb4 Rxh5 4.Rc6+ and white can continually check Blacks king if it stays on the kingside, and if it comes over to the queenside, the Black rook will be stuck defending it's pawn from the front.

Black can do nothing as long as White's king stays on a2 and b2, and the White rook checks the Black king if it touches his pawn. Notice that White king cannot leave the 2nd rank(1.Kb3 Rb1+ and 2...h1/Q) or move to the c-file (1.Kc2 Ra1. 2.Rxh2 Ra2+ picking up the White rook).