In the diagram, which must be true for point d to be an orthocenter?
be, cf, and ag are angle bisectors.
be ⊥ ac, ag ⊥ bc, and cf ⊥ ab.
be bisects ac, cf bisects ab, and ag bisects bc.
be is a perpendicular bisector of ac, cf is a perpendicular bisector of ab, and ag is a perpendicular bisector of bc.
!

A copy of the diagram is shown below

Point D is the intersection of three angle bisector. 
BE is the angle bisector of ∠B
CF is the angle bisector of ∠C
AG is the angle bisector of ∠A

Point D is also the intersection between three perpendicular bisector
BE is the perpendicular bisector of AC
AG is the perpendicular bisector of BC
CF is the perpendicular bisector of AB

Hence the correct statements is statement 1 and statement 4