Question

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

Explanation:

Step1: Recall Midsegment Theorem

A midsegment of a triangle connects the midpoints of two sides. So, \( P \) is the midpoint of \( \overline{MN} \) and \( O \) is the midpoint of \( \overline{ML} \) (since \( \overline{PO} \) is a midsegment of \( \triangle LMN \)).

Step2: Analyze Midpoint Property

By the definition of a midpoint, a midpoint divides a segment into two congruent segments. For segment \( \overline{ML} \), \( O \) is the midpoint, so \( \overline{MO} \cong \overline{OL} \).

Answer:

B. \( \overline{OL} \) (assuming the options are labeled as A: \( \overline{MP} \), B: \( \overline{OL} \), C: \( \overline{PN} \), D: \( \overline{PO} \))