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Constructing a Parallel Line through an Inaccessible Point

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Given a straight line and two lines and that intersect at an inaccessible point , construct a straight line through parallel to . You can drag or .

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The general method for solving this problem is to use a transformation so that the inaccessible point becomes the accessible point . In this case, the transformation is a translation in the direction of .

Using the slider, translate and parallel to to and such that the corresponding translates of and intersect at the accessible point .

Then draw the line through parallel to .

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

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Reference

[1] B. I. Argunov and M. B. Balk, Elementary Geometry (in Russian), Moscow: Prosveščenie, 1966 pp. 338–339.

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