To solve this problem, let’s analyze the situation step by step:

Given Information:

1. Triangle $JKL$ is formed by connecting the midpoints of the sides of triangle $GHI$.
2. The lengths of the sides of $GHI$ are:
   • $GH = 14$,
   • $HI = 18$,
   • $IG = 8$.

Key Property of the Midsegment Theorem:

When a triangle is divided by connecting the midpoints of two of its sides:

• The line segment (midsegment) is parallel to the third side.
• The length of the midsegment is half the length of the third side.

Application of the Theorem:

• In this case, $LK$ is the midsegment of triangle $GHI$ and is parallel to side $GH$.
• Therefore: $LK = \frac{1}{2} \times GH$ Substituting $GH = 14$: $LK = \frac{1}{2} \times 14 = 7$

Final Answer:

The length of $LK$ is: $\boxed{7}$

Would you like a more detailed explanation or additional examples?

5 Related Questions:

1. How do we calculate the length of other midsegments in triangle $GHI$?
2. What happens if triangle $GHI$ is an equilateral triangle?
3. Can we use the Midsegment Theorem in 3D geometry?
4. What are the properties of triangle $JKL$ formed by the midpoints of $GHI$?
5. How is the area of triangle $JKL$ related to triangle $GHI$?

Tip:

Always look for midpoint connections in triangles to apply the Midsegment Theorem for solving parallel and length-related problems.