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This page uses JavaSketchpad. You may drag any of the red points, and the construction will adjust accordingly.

Explanation of the construction: Looking at the final configuration, one can see that the slant transversal distance AB between lines FG and IH must be the same as the slant distance on the 90 degree rotated transversal between lines FI and GH. So we construct the rotated transversal BE and measure off distance AC to find point E.

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