Cynthia Joan Gastelle left her Takoma Park home on the morning of April 3, 1980, her family said, headed for job interviews in Silver Spring. The diminutive 18-year-old made it to one appointment, at a delicatessen, and then disappeared.

Cynthia’s father reported her missing, and for more than 30 years, the Gastelle family searched for her, making agonizing trips to morgues and fielding tips from across the country. Each lead turned up cold.

On Wednesday, authorities announced that DNA from skeletal remains found in 1982 — in what was then a remote section of Prince William County — was Cynthia’s. For her relatives, some of whom attended the news conference, the discovery did not bring closure but a fresh wound: Cynthia, described by her brother Peter as a “beautiful and vibrant” girl who loved to dance, had been killed.

“We had so hoped that she would come back to us,” said Peter Gastelle, whose voice cracked as he spoke. “Our hope is now gone, and our hearts are broken again.”

Peter Gastelle and police issued an appeal to the public for leads in the long-standing mystery. Emphasizing the many years that have passed, Gastelle — with a shock of white hair — stood next to a portrait of his sister, who had long, feathered blond locks.

Cynthia Joan Gastelle (Courtesy of Prince William police)

Cynthia would have been 49, if she had lived. Gastelle, who was accompanied by a brother and sister Wednesday, said his parents died without knowing what happened to their youngest child.

Prince William police said the break in the case came after DNA samples were collected from the Gastelle family in 2011 to see whether the material matched DNA from remains found in another jurisdiction.

There was no hit in that case, but the Virginia medical examiner notified police in May that the family’s samples matched remains discovered in Prince William.

Authorities credited advances in forensic science for the hit. The match was produced by a type of test that uses mitochondrial DNA and that has been used in Virginia only since 2008.

A hiker stumbled upon the remains in a wooded area in the 1100 block of Mountain Road, near Haymarket, in February 1982. The skeleton showed injuries consistent with a stabbing, police said. A cream-colored sweater and dark corduroy pants were found with the remains, police said. Cynthia stood 5-foot-1 and weighed about 90 pounds.

Detectives said they want to speak with Cynthia Gastelle’s former boyfriend, a man who was called Mike or Michael and who was a part-time student in his late teens or early 20s at the time of her disappearance. Police said they are unsure of his full name, but they showed a photo of him in which he has long, curly hair, lambchop sideburns, a goatee and mustache. They emphasized that he is not a suspect in the case.

Cynthia, who had recently received a general equivalency diploma from Montgomery Blair High School and a cosmetology certificate, left home about 10:30 that April morning in 1980 and boarded a Ride On bus to Silver Spring, Peter Gastelle said. There were no hints that she was in trouble before she vanished, relatives said.

Takoma Park police interviewed relatives and friends and checked records in the days and weeks that followed, but no sign of Cynthia turned up. In 2001, her DNA was entered in a national database, and police have periodically asked the public for help with the case.

Police said it is unclear how she ended up in Prince William, about 45 miles from her home. “We don’t see any connection between Cynthia Gastelle and Northern Virginia,” said Detective Brian Cody of the Prince William police.

On the day Cynthia disappeared, her father received a call from the Silver Spring deli where she had interviewed for a job, Peter Gastelle said. The owner of the deli informed Terrence Gastelle that his daughter had gotten the job.

“Cindy, we love you — always have and always will,” Peter Gastelle said. “We hope you are at peace.”