Episode 11 of "Angel"
s01e11 Somnambulist

A girl is murdered by a vampire during the early morning hours. Later that day, Wesley notices an article about the murder in the newspaper and leaves immediately. Angel pays a visit to Kate about some other business, but while he is there, he observes the crime scene photos on her desk. He recognizes the modus operandi, and immediately realizes that there is a connection between his recent nightmares and the murders. Meanwhile, Wesley returns to Angel Investigations and clues Cordelia in on the situation at hand. He tells her in the past, Angelus marked his victims' left cheek with a cross. That night, Angel has a dream. He realizes that Penn, someone he sired, is responsible for the current murders. That afternoon, Angel brings a drawing of Penn to Kate and instructs her to stake out an area. Later that day, Penn strikes, but before he can complete the kill, the police arrive. Penn escapes in a nearby abandoned building. Kate comes in after him and soon finds Angel at the scene. He dons his vampire face and the two begin to fight. After learning Angel's true identity, Kate initially freaks out, but then hits the library to learn more about vampires. She discovers that Penn struck two times in LA earlier that century, in 1928 and 1963. Wesley and Angel figure out where he resides and pay a visit to his apartment. Meanwhile, Penn pays a surprise visit to the police department. Angel catches wind of the situation climbs down into the tunnels and gets into a big brawl with Penn. However, it's Kate who saves the day when she locates a wood scrap and stakes Angel and Penn. Due to her great aim, only Penn is dusted.