Constructing a Line through a Given Point and an Inaccessible Point

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Given a point and two lines , that intersect at an inaccessible point , construct a straight line through and .


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.


Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA



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].


[1] B. I. Argunov and M. B. Balk, Elementary Geometry (in Russian), Moscow: Prosveščenie, 1966 p. 337.

[2] H. R. Jacobs, Geometry, New York: W. H. Freeman & Company, 1987.

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