refer to the image below. point w in triangle qrs indicates the triangles centroid. the interior line segments are the medians of triangle qrs. which statement about triangle qrs is true? segment qt is congruent to segment tr. segment qw is congruent to segment wu. segment qw is congruent to segment wt. segment wr is congruent to segment qv.

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# Brief Explanations:
1. Recall the property of a centroid in a triangle: The centroid divides each median into a ratio of $2:1$, with the longer segment being closer to the vertex. Also, a median connects a vertex to the midpoint of the opposite side, so the midpoint divides the side into two congruent segments.
2. Analyze each option:
   - Option 1: Segment $QT$ and $TR$ – $RT$ is a median? Wait, no, the medians are $QU$, $SV$, $RT$? Wait, no, the medians are the lines from each vertex to the midpoint of the opposite side. So, for example, $QU$ is a median, so $U$ is the midpoint of $SR$, $V$ is the midpoint of $QS$, and $T$ is the midpoint of $QR$. So $QT = TR$ because $T$ is the midpoint of $QR$. Wait, let's re - check:
     - A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. So if $RT$ is a median, then $T$ is the midpoint of $QR$, so $QT = TR$. Wait, but let's check the other options too.
   - Option 2: Segment $QW$ and $WU$ – The centroid $W$ divides the median $QU$ in the ratio $2:1$, so $QW=\frac{2}{3}QU$ and $WU = \frac{1}{3}QU$, so $QW$ is not congruent to $WU$.
   - Option 3: Segment $QW$ and $WT$ – There is no property that says these are congruent. $QW$ is part of the median $QU$, and $WT$ is part of the median $RT$ (or another median), so they don't have to be congruent.
   - Option 4: Segment $WR$ and $QV$ – $WR$ is part of the median from $R$ to $V$ (midpoint of $QS$), and $QV$ is half of $QS$ (since $V$ is the midpoint). There's no reason for them to be congruent.

So the correct statement is that segment $QT$ is congruent to segment $TR$ because $T$ is the midpoint of $QR$ (since $RT$ is a median, connecting $R$ to the midpoint of $QR$'s opposite side? Wait, no, $QR$'s opposite side is $QS$? Wait, no, in triangle $QRS$, the vertices are $Q$, $R$, $S$. So the side opposite $Q$ is $SR$, opposite $R$ is $QS$, and opposite $S$ is $QR$. So the median from $R$ should go to the midpoint of $QS$ (which is $V$), the median from $S$ should go to the midpoint of $QR$ (which is $T$), and the median from $Q$ should go to the midpoint of $SR$ (which is $U$). So $T$ is the midpoint of $QR$, so $QT = TR$.
# Answer:
Segment QT is congruent to segment TR.

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