2.22 - [i]Any two coplanar lines have at least one common point.[/i] PROOF. Let E be a point coplanar with the two lines but not on either of them. Let [i]AC[/i] be one of the lines. Since the plane [i]ACE[/i] is determined by the pencil of lines through [i]E[/i] that meet [i]AC[/i], the other one of the two given lines may be taken to join two points on distinct lines of this pencil, say [i]B[/i] on [i]EA[/i], and [i]D[/i] on [i]EC[/i], as in the figure provided. According to Axiom 2.14, the two lines [i]AC[/i] and [i]BD[/i] have a common point.