Question

m is the centroid of def.
dm = 8, mj = 2y, em = 6, fm = 2x
\overline{dk}, \overline{el}, and \overline{fj} are ______.
\bigcirc medians
\bigcirc altitudes
\bigcirc angle bisectors
\bigcirc perpendicular bisectors

Explanation:

A median of a triangle is a segment from a vertex to the midpoint of the opposite side. The centroid (M) is the intersection of the medians, and it divides each median into a ratio of 2:1 (from vertex to centroid : centroid to midpoint). Here, \( \overline{DK} \), \( \overline{EL} \), and \( \overline{FJ} \) connect vertices (D, E, F) to midpoints (K, L, J) of opposite sides (since M is the centroid, these segments must be medians). Altitudes are perpendicular to opposite sides, angle bisectors split angles, and perpendicular bisectors are perpendicular to and bisect sides (not from vertices to midpoints in the same way as medians). So the correct term is medians.

Answer:

A. medians