Question

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.

Explanation:

The orthocenter of a triangle is the point of intersection of the triangle's altitudes. An altitude is a line segment from a vertex of the triangle perpendicular to the opposite side. So for point D to be the orthocenter, the lines BE, AG, and CF must be perpendicular to the opposite sides AC, BC, and AB respectively.

Answer:

BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB.