Question

Triangle A B C is shown. Lines are drawn from each point to the opposite side and intersect at point D. They form line segments A G, B E, and C F.
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.

Answer 1

BE ⟂ AC, AG ⟂ BC, and CF ⟂ AB.

Reason: the orthocenter is the intersection of the triangle's altitudes, so the segments from each vertex to the opposite side must be perpendicular to those sides.