How we cite our quotes:
Quote #7
"If you confront anyone who has lied with the truth, they usually admit it – often out of sheer surprise. It is only necessary to guess right to produce your effect." (3.5.63)
Again, one of Poirot's major weapons is human psychology. He's figured out how to catch people in a lie.
Quote #8
"I wished to ask you, Mademoiselle, why you lied to us this morning?"
"Lied to you? I don't know what you mean."
"You concealed the fact that at the time of the Armstrong tragedy you were actually living in the house. You told me that you had never been in America."
He saw her flinch for a moment and then recover herself. (3.7.5-8)
Poirot confronts Mary Debenham with the truth, and her reaction, however slight her flinch may be, gives her away.
Quote #9
"This," said Dr. Constantine, "is more wildly improbably than any roman policier I have ever read." (3.8.59)
Dr. Constantine compares the plot to a roman policier, or a police novel. This is a very meta thing to do, isn't it? The fiction is calling attention to itself as fiction.