Three perpendicular theorem

Theorem .

If a straight line drawn on a plane through an inclined base is perpendicular to its projection, then it is perpendicular to an inclined one.



Proof .

Let AB be perpendicular to the plane α, AC be tilted and c be a straight line in the plane α, passing through the base C tilted. Let's draw a straight line CA` parallel to straight line AB. It is perpendicular to the plane α. Draw the plane β through the lines AB and A`C. Straight line with perpendicular line CA`. If it is perpendicular to the line CB, then it is perpendicular to the plane α, and hence the line AC.