Which statement is always true about the segments in triangle JKL?

Question

anonymous · Answer

Look at the acute triangle JKL. Point O is the centroid and S is the orthocenter.
 Which statement is always true about the segments in triangle JKL?

Possible Answers: 		Segment LM is the same length as segment LN.
		Segment LS is the same length as segment SM.
		Segment LO is two-thirds the length of segment LN.
		Segment LS is two-thirds the length of segment LM.

anonymous · Answer

attachment

directrix · Answer

Segment LO is two-thirds the length of segment LN.
---
Segment LN is a median as evidenced by the presence of O, the centroid. The centroid is the point of concurrency of the medians of a triangle and divides a given median into a 2:1 ratio. Hence, LO = 2/3 of LN.