Question

based on the given diagram, complete the sentence below.

answer attempt 1 out of 3

point d is the of △abc because \\(\overline{de}\\), \\(\overline{df}\\), and \\(\overline{dg}\\) are all

Explanation:

In a triangle, the incenter is the point equidistant from all three sides, and this distance is the length of the perpendicular from the incenter to each side. Here, \( \overline{DE} \), \( \overline{DF} \), and \( \overline{DG} \) are perpendicular to the sides of \( \triangle ABC \) (as indicated by the right angles) and should be equal in length (since \( D \) is equidistant from all sides), so \( D \) is the incenter. Also, the markings on the sides suggest \( G \) is a midpoint of a segment with equal markings, \( F \) is on a side with equal segment markings, and \( E \) is on another side with equal segment markings, but the key is the perpendicular distances from \( D \) to each side, which defines the incenter.

Answer:

incenter