The Three Perpendiculars Theorem

In spatial geometry, the following relationships between lines and planes hold true, and they are known as the Three Perpendiculars Theorem.

In the figure, consider a point that is not on the plane , a line on the plane , a point on line , and a point on the plane but not on line .

1. If and , then .
   (If is perpendicular to the plane and is perpendicular to line , then is also perpendicular to line .)
2. If and , then .
   (If is perpendicular to the plane and is perpendicular to line , then is also perpendicular to line .)
3. If , , and , then .
   (If and are perpendicular to line , and is perpendicular to , then is perpendicular to the plane .)