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Two Triangles are perspective from a line if the extensions of their three pairs of corresponding sides meet in Collinear points. The line joining these points is called the Perspective Axis. Two Triangles are perspective from a point if their three pairs of corresponding Vertices are joined by lines which meet in a point of Concurrence. This point is called the Perspective Center. Desargues' Theorem guarantees that if two Triangles are perspective from a point, they are perspective from a line.
See also Desargues' Theorem, Homothetic Triangles, Paralogic Triangles, Perspective Axis, Perspective Center