Madison Keys closed in on an Olympic tennis medal by reaching the women's singles semifinals Thursday, then scampered from Court 1 to Court 4.

She wanted to make sure she would get there in time to sit in the stands and cheer for U.S. teammate Steve Johnson during the closing minutes of a victory that put him in the men's quarterfinals.

Shortly after that, Johnson and Keys sought each other out in the interview area to share smiles and an enthusiastic high-five. A Rio de Janeiro Games tournament that began inauspiciously for the Americans was suddenly looking a lot better Thursday.

The No. 7-seeded Keys' power-based game overwhelmed Daria Katsatkina of Russia 6-3, 6-1 in a mere 53 minutes, thanks in large part to a 30-4 edge in winners. Earn one more victory — either in the semifinals against No. 2 Angelique Kerber of Germany, or in the bronze match — and Keys will head back home with a medal.

"The first thing I did was say, 'Yes, I won!'" Keys said. "And then I was like, 'What's Stevie's score?'"

Johnson, a four-time NCAA team champion and two-time individual winner for Southern California, had a similarly easy time of things against Evgeny Donskoy of Russia, winning 6-1, 6-1.

Johnson said he noticed Keys supporting him at courtside over the final couple of games.

"When we're at the Grand Slams, it's tough for us to go out and watch just because it's so busy and whatnot. I'm always rooting for the Americans to do well, regardless of who they are," he said. "To see her doing well here, hopefully she's going to get one more and get to the final and do some damage."

Next for Johnson comes a far more daunting task: He will play No. 2 Andy Murray, the defending Olympic gold medalist and a three-time Grand Slam champion with a semifinal berth on the line.

They've met only once before, with Murray winning in straight sets last year.

"Any given day, you can beat anybody," said Johnson, who is seeded 12th. "So I'll go out there with a different gameplan and the right mindset."

Johnson also still is in the running for a medal in men's doubles.

He and partner Jack Sock lost 6-3, 7-5 to Florin Mergea and Horia Tecau of Romania in the semifinals, but can head home with a bronze if they beat Daniel Nestor and Vasek Pospisil of Canada.

Sock is part of one of two mixed doubles teams that could earn a medal for the United States, too.

He and Bethanie Mattek-Sands reached the quarterfinals of that 16-team event, and so did Venus Williams and Rajeev Ram, by winning in the first round Thursday. Mattek-Sands and Sock defeated Johanna Konta and Jamie Murray of Britain 6-4, 6-3, while Williams and Ram got past the Dutch pair of Kiki Bertens and Jean-Julien Rojer 6-7 (4), 7-6 (3), 10-8.

Williams lost in the first round of singles and women's doubles in Rio. Her sister Serena, the defending champion in both of those events, exited in the third round of singles.

"What can you do, except come back and play again?" Williams said.

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