He denied the Garda suggestion that it was so she wouldn't tell people he had raped her.
"I just strangled her with my two hands around her neck," he said. "I killed her in the livingroom."
He said the children were asleep when he brought their mother's body into the bedroom.
"I sat on the bed. I didn't know what to do," he said. "I saw the kids. It made me more sad that I'd taken their mother away on Christmas."
"I don't know why I did it," he said about setting two fires. "I never thought about the children. I was worried about the murder."
He said he knew what he had done to the Whelan family was unbearable. "I will never be able to cope with this so God help them," he said. "I'm so, so sorry. I don't know what else to say."
Det Sgt Jim Lyng agreed that the prosecution's case was that rape was the trigger for the killing, that "he killed her, then sat there, pondered what he'd do next and set the fires".
He agreed with Paul Coffey SC, defending, that Hennessy was from a respectable family and had never been in trouble. Det Sgt Lyng also agreed that the defendant had worked four consecutive night shifts and had slept only briefly after coming home from work on Christmas Eve before spending 10 hours drinking.
Sharon Whelan's brother, John Whelan, described the murders as inhuman. "It's obvious human life means nothing to you," he told Hennessy from the witness box. "It's beyond belief that anyone with a conscience could contemplate, never mind carry out such evil."
He told the court that his father used to collect Zara from school every day, while Sharon and Nadia spent most days with his mother.
Mr Whelan said Christmas, which had meant so much to his sister and nieces, was now a time of loss and profound grief for his family.
He said the little girls "never woke from their sleep" to find it was Christmas morning.
"The murder of our girls has left a hole in our hearts," he said, explaining that every morning and every night his parents made the two-minute walk to their graves to chat to them. "It's all they have left. They hear children playing in the local school every day, knowing Zara should be there.
"The pain is overwhelming," he said. "All you will lose is your liberty, a loss that does not come close to the loss you have imposed on this family," he told Hennessy.
Afterwards, Mr Whelan told reporters that Hennessy's admission had meant they did not have to go through a long trial.
He also said that his family bore no animosity toward the Hennessy family. "They cannot be held responsible for one man's actions," he said.