If two straight lines be at right angles to the same plane, the straight lines will be parallel.
Proof
Suppose the two perpendiculars AB, CD met or were skew. Drop
the segment BD in the plane; the angles at B and D are right.
In the plane through AB and BD, by I.28 the line CD would
need to be parallel to AB, fixing the plane through AB, CD.
Then within that plane the two right angles force AB∥CD.