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:

Step1: Recall the definition of the orthocenter

The orthocenter of a triangle is the point where the three altitudes of the triangle intersect.

Step2: Identify the altitudes in the diagram

In the given diagram of \(\triangle ABC\), \(\overline{AF}\), \(\overline{BG}\), and \(\overline{CE}\) are all altitudes (each is perpendicular to a side of the triangle).

Step3: Determine the point of intersection of the altitudes

Since point \(D\) is the intersection of the three altitudes \(\overline{AF}\), \(\overline{BG}\), and \(\overline{CE}\), by the definition of the orthocenter, point \(D\) is the orthocenter of \(\triangle ABC\).

Answer:

orthocenter