In triangle $FGH$, points $J$ and $K$ are the midpoints of sides $FG$ and $GH$, respectively. If $FH$ has length $10$ and the segment $JK$ is parallel to $FH$, what is the length of $y$, where $y$ is the length of $JK$?

• A. $10$
• B. $7$
• C. $5$
• D. $15$

Answer: (C)

Verified step by step guidance

1. Identify that points J and K are midpoints of sides FG and GH respectively in triangle FGH.
2. Recall the Midsegment Theorem in triangles, which states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and its length is half the length of that third side.
3. Since JK connects the midpoints J and K, segment JK is parallel to side FH and its length y is half the length of FH.
4. Write the relationship using the Midsegment Theorem: \(y = \frac{1}{2} \times FH\).
5. Substitute the given length of FH (which is 10) into the equation to express y in terms of known values: \(y = \frac{1}{2} \times 10\).