Question

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

Explanation:

Step1: Recall Midsegment Property

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

Step2: Analyze Congruent Segments

As \( O \) is the midpoint of \( ML \), it divides \( ML \) into two equal parts: \( MO = OL \).

Step3: Evaluate Options

• \( \overline{MP} \): \( P \) is midpoint of \( MN \), so \( MP = PN \), not related to \( MO \) directly.
• \( \overline{OL} \): Since \( O \) is midpoint of \( ML \), \( MO = OL \).
• \( \overline{PN} \): \( PN = MP \), not equal to \( MO \).
• \( \overline{PO} \): \( PO \) is a midsegment, length related to \( LN \), not equal to \( MO \).

Answer:

\( \overline{OL} \) (or the option corresponding to \( \overline{OL} \))