RIO DE JANEIRO — Scroll back to 2011 for a minute. In the quarterfinals of the Women’s World Cup, with the United States down a goal and a player in the final seconds of overtime, Megan Rapinoe curled a 45-yard crossing pass onto the forehead of Abby Wambach, who smashed it into the net for a 2-2 tie in a game that the Americans won on penalty kicks.

The degree of difficulty alone made it one of the great goals in United States soccer history — think of sinking a 50-foot putt on the 18th green to win the United States Open — and it propelled Rapinoe and Wambach, and their teammates, to the final, where they had a 2-1 lead late in overtime against Japan but could not protect it as Japan won on penalty kicks.

Check out 2012 for a second. At the Summer Olympics in London, the same group of American women fought off a huge upset bid by Canada in the semifinals, finally prevailing, 4-3, when Alex Morgan headed in the winning goal, again in the final seconds of overtime. This time the United States held onto a 2-1 lead against Japan in the finals, only because Hope Solo made a great body-extension save in the final minutes of regulation to prevent a tying goal.