Perpendicularity of a Line & a Plane Lesson 6.2

Definition: A line is ⊥ to a plane if it is ⊥ to every line in the plane that passes through its foot. A AB ⊥ BD C B E D If AB ⊥ m, then AB ⊥ BC AB ⊥ BD and AB ⊥ BE. m

Prove a line ⊥ to a plane Theorem 48: If a line is ⊥ to two distinct lines that lie in a plane and that pass through the foot, then it is ⊥ to the plane. A C B D m

If <STR is a right angle, can you conclude ST ⊥ m ? NO!!!, to be ⊥ it must be ⊥ to at least 2 lines that lie on m and pass through T

PF  k PF  FG, PF  FH  PFG is a rt  PFH is a rt  PG  PH PF  PF ΔPFG  ΔPFH G  H Given If a line is  to a plane, it is  to every line in the plane that passes through its foot.  lines form rt s Reflexive Property HL (3,4,5) CPCTC