Matching geometric symbols with their corresponding diagrams.

To solve this problem, we need to match each symbol or description in the left column with the corresponding diagram in the right column. Let's go through each problem step by step.

Problem 1: \( \overleftrightarrow{AW} \)

- This represents a line passing through points \( A \) and \( W \).
- Diagram F shows a line with points \( B, W, \) and \( A \) on it, which matches \( \overleftrightarrow{AW} \).

Problem 2: Noncollinear points \( J, K, L \)

- Noncollinear points are points that do not lie on the same line.
- Diagram C shows points \( J, K, \) and \( L \) not lying on the same line, which matches the description.

Problem 3: \( \overrightarrow{BW} \)

- This represents a ray starting at point \( B \) and passing through point \( W \).
- Diagram D shows a ray starting at \( B \) and passing through \( W \), which matches \( \overrightarrow{BW} \).

Problem 4: A ray with endpoint \( J \)

- This represents a ray starting at point \( J \).
- Diagram J shows a ray starting at \( J \), which matches the description.

Problem 5: \( \overrightarrow{BA} \)

- This represents a ray starting at point \( B \) and passing through point \( A \).
- Diagram I shows a ray starting at \( B \) and passing through \( A \), which matches \( \overrightarrow{BA} \).

Problem 6: Opposite rays \( \overrightarrow{JK} \) and \( \overrightarrow{JL} \) (180° "direction change")

- Opposite rays start at the same point and extend in opposite directions.
- Diagram H shows two rays \( \overrightarrow{JK} \) and \( \overrightarrow{JL} \) starting at \( J \) and extending in opposite directions, which matches the description.

Problem 7: Collinear points \( J, K, L \)

- Collinear points are points that lie on the same line.
- Diagram A shows points \( K, L, \) and \( J \) lying on the same line, which matches the description.

Problem 8: \( \overrightarrow{WA} \)

- This represents a ray starting at point \( W \) and passing through point \( A \).
- Diagram E shows a ray starting at \( W \) and passing through \( A \), which matches \( \overrightarrow{WA} \).

Problem 9: \( \overrightarrow{AW} \)

- This represents a ray starting at point \( A \) and passing through point \( W \).
- Diagram G shows a ray starting at \( A \) and passing through \( W \), which matches \( \overrightarrow{AW} \).

Problem 10: \( \overline{BA} \)

- This represents a line segment between points \( B \) and \( A \).
- Diagram E shows a line segment between \( B \) and \( A \), which matches \( \overline{BA} \).

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & F \\
2. & C \\
3. & D \\
4. & J \\
5. & I \\
6. & H \\
7. & A \\
8. & E \\
9. & G \\
10. & E \\
\end{array}
}
\]