Question

recognizing relationships within a triangle
given that (overline{po}) is a midsegment of (\triangle lmn), to which segment is (overline{mo}) congruent?
(overline{mp})
(overline{ol})
(overline{pn})
(overline{po})

Explanation:

A midsegment of a triangle connects the midpoints of two sides. Since $\overline{PO}$ is a midsegment of $\triangle LMN$, $P$ and $O$ must be midpoints of $\overline{MN}$ and $\overline{ML}$ respectively. As the midpoint of $\overline{MN}$, $P$ divides $\overline{MN}$ into two congruent segments: $\overline{MP} \cong \overline{PN}$. The question asks for the segment congruent to $\overline{MP}$, so $\overline{PN}$ is the answer.

Answer:

PN