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.

THIS USER ASKED 👇

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.

THIS IS THE BEST ANSWER 👇

BE, CF and AG are angle bisectors. Thus, their meeting point I, is the incentive of the triangle ABC.

BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB. Thus, O, orthocentre of the triangle ABC is the meeting point of BE, CF and AG.

BE bisects AC, bisects CF AB, and AG bisects BC. Thus, BE, CF and AG are medians and their meeting point is G, the center of the triangle ABC.

From the above, it is clear that I = O = G.

This property is only good for equilateral triangles.

Hence, ABC is an equilateral triangle.