If a straight line be set up at right angles to two straight lines which cut one another, at their common point of section, it will also be at right angles to the plane through them.
Proof
Take any other straight line ℓ through the foot in the plane;
ℓ can be expressed as a sum of perpendicular components on the
two given lines (by I.46-style decomposition), and the perpendicular
to both is perpendicular to the sum by I.4 applied to the right
triangles formed.