Question

based on the given diagram, complete the sentence below.
answer attempt 1 out of 2
point ( d ) is the of ( \triangle a b c ) because ( overline{a f}, overline{b g} ), and ( overline{c e} ) are all

Explanation:

The in - center of a triangle is the point of intersection of the angle bisectors. However, in this case, since \(AF\), \(BG\), and \(CE\) are perpendicular to the sides of the triangle (\(AF\perp BC\), \(BG\perp AC\), \(CE\perp AB\)), they are the altitudes of the triangle. The ortho - center of a triangle is the point of intersection of the altitudes of the triangle.

Answer:

Point \(D\) is the ortho - center of \(\triangle ABC\) because \(\overline{AF}\), \(\overline{BG}\), and \(\overline{CE}\) are all altitudes.