Constructing a Line through a Given Point and an Inaccessible Point
Given a point and two lines , that intersect at an inaccessible point , construct a straight line through and .[more]
Let the line through intersect and at and , respectively.
You can drag or or move with the slider.
Let be another point on .
Let a line parallel to intersect and at and , respectively.
Draw the segments and .
Let be the intersection of with a straight line through that is parallel to .
Let be the intersection of and the straight line through that is parallel to .
The extension of the segment is the desired line.
We have since by the side-splitter theorem.[less]
The side-splitter theorem states: if a line parallel to one side of a triangle intersects the other two sides at different points, it divides the sides in the same ratio [2, p. 354].
 B. I. Argunov and M. B. Balk, Elementary Geometry (in Russian), Moscow: Prosveščenie, 1966 p. 337.
 H. R. Jacobs, Geometry, New York: W. H. Freeman & Company, 1987.