Now, since BC is at right angles to each of the straight lines DA, DE,
therefore BC is also at right angles to the plane through ED, DA. [XI. 4]
And GH is parallel to it;
but, if two straight lines be parallel, and one of them be at right angles to any plane, the remaining one will also be at right angles to the same plane; [XI. 8]
therefore GH is also at right angles to the plane through ED, DA.
Therefore GH is also at right angles to all the straight lines which meet it and are in the plane through ED, DA. [XI. Def. 3]
But AF meets it and is in the plane through ED, DA;
therefore GH is at right angles to FA,
so that FA is also at right angles to GH.
But AF is also at right angles to DE;
therefore AF is at right angles to each of the straight lines GH, DE.
But, if a straight line be set up at right angles to two straight lines which cut one another, at the point of section, it will also be at right angles to the plane through them; [XI. 4]
therefore FA is at right angles to the plane through ED, GH.
But the plane through ED, GH is the plane of reference;
therefore AF is at right angles to the plane of reference.