RIO DE JANEIRO — They indeed are the Odd Couple of gymnastics. One comes from Massachusetts, the other from Texas. One is four inches taller, the other three years younger. One is black, the other is white.

But when the Olympic competition ended here on Tuesday afternoon, Simone Biles and Aly Raisman were standing alongside each other yet again, great friends who just happen to be the best two performers on the planet.

“We put the cherry on top, me and Aly,’’ Biles declared after she and Raisman had swept the floor exercise to cap the greatest Games ever for the United States women’s squad, a nine-medal motherlode that included golds in the team, all-around, and vault events.

It was the most dominant showing by one country since the Soviet Union squad won 10 medals in 1972 behind Ludmila Turishcheva and Olga Korbut. Three of the four times that the United States anthem was played, the 19-year-old Biles and the 22-year-old Raisman were on the podium together in joyful juxtaposition. One of them was too young for the London Games four years ago. The other was considered by many to be too old for Rio.

But even before the team was picked last month, Biles and Raisman had formed a close bond, each of them enormously impressed with and amused by the other.

“I remember watching her in 2012 and I was, like, I want to be just like her,’’ said Biles. “So to be able to stand next to her I feel like I’m just like her.’’

The most notable difference between them is that Biles, the three-time world champion, was expected to dominate these Games, and she did with a record-tying four golds and a bronze.

“I can’t believe that she has four gold medals,’’ marveled Raisman, who earned a gold and two silvers. “It’s amazing. It’s hard to put into words. I don’t even consider myself competing against her. She’s just incredible. I’m in awe watching her.’’

Raisman, who took a year off after London, defied significant odds even to make a second team. “There were a lot of ups and downs, sometimes deep downs, but we managed to bring her back and to support her,’’ said Mihai Brestyan, Raisman’s coach.

Raisman not only worked her way back to her old Olympic form, she improved upon it. During the national championships and Olympic trials she was the veteran voice urging nervous teenagers to relax and enjoy moments that millions of girls dream about. Biles dubbed her “Grandma Aly’’ and made fun of her relative cluelessness about social media and her early bedtime.

“The other night I went in her room and she got mad after I asked her to be quiet,’’ Raisman said. “I said, it’s 9:45. I don’t think it’s that crazy for me to ask you to be quiet.’’ “I said, Aly, that’s like 12 hours of sleep,’’ Biles said. “You’re fine. It’s not hibernating time. We always tell Aly, you can sleep when you’re dead.’’

When the time came to chalk up with the medals on the line, the well-rested Raisman submitted the best routines of her life. She outpointed teammate and London champion Gabby Douglas to make the all-around final, then collected the medal that she’d lost on a tiebreaker last time.

To Raisman it was a silver that was as good as gold. Nobody in the world had beaten Biles in three years.

“After all-around, Laurie [Hernandez] said, if you get silver again you’re the best, because Simone doesn’t count,’’ Raisman said.

Raisman had won the floor gold in London but Biles had claimed the last three world titles and had a more difficult program. By the time that Raisman stepped up as the next-to-last competitor, Biles already had turned in a thunderous routine that earned her a score of 15.966 that was the best ever under the current format.

“Smile, enjoy and just make a show with your head up on the stage,’’ Brestyan said he told his pupil. “That’s what it’s all about — and that’s what she did.’’

Raisman’s tally of 15.500 was her best of the Games in the event and more than half a point better than that of British bronze medalist Amy Tinkler.

“I did the best I can possibly do,’’ she said after kissing her medal and giving an exuberant thumb’s up on the award stand.

The silver brought her Olympic total to half a dozen — three golds, two silvers and a bronze. It was a performance befitting a grand exit from the world stage but Raisman, by far the oldest US women’s gymnast to win a gold medal, wasn’t ruling out continuing on for a third Games in Tokyo in 2020.

“That’s what everyone’s saying now, so I just said that I get better with age, so maybe I will,’’ said Raisman, who’ll be 26 then. “It’s obviously very hard to get to this point and it’s not always fun getting back to this crazy shape that we’re in right now. But I love gymnastics, I enjoy competing and I think I surpassed my expectations and everyone else’s. I’m definitely on a high right now but I think I’ll take some time off, take a break and then will come back to the gym and see how it goes.’’

Biles, who’s the fifth female gymnast to win four golds at one Games, wouldn’t say whether she was the greatest of all time.

“I would never rank myself,’’ she said. “It’s weird.’’ But having also already collected 10 world gold medals and with no obvious challenger on the horizon, Biles wouldn’t appear to have much incentive to continue for another quadrennium. “I think my passion and my love for the sport would keep me there,’’ she said.

If so, the Odd Couple may well be up for a golden reprise.

“I think [Raisman] has accomplished so much and I think she’s ready to move on, but I don’t know,’’ Biles said. “Aly’s pretty crazy and she might be there.’’

John Powers can be reached at john.powers@globe.com.