L and M are respectively the points on the sides DE and DF of a triangle DEF, such that DL = 4, `LE=4/3,DM=6` and `DF=8`. Is `Lmabs()EF`? Give reason.

Answer

To determine if line segment LM is parallel to line segment EF in triangle DEF, we can use the Basic Proportionality Theorem (also known as Thales' theorem). According to this theorem, if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

### Step-by-Step Solution:

1. **Identify the Given Lengths:**
- DL = 4
- LE = 4/3
- DM = 6
- DF = 8

2. **Calculate the Length of EF:**
- Since DF = DM + MF, we can find MF:
\[ MF = DF - DM = 8 - 6 = 2 \]

3. **Set Up the Proportionality Ratios:**
- According to the Basic Proportionality Theorem, we need to check if:
\[ \frac{DL}{LE} = \frac{DM}{MF} \]

4. **Calculate the Ratios:**
- Calculate \( \frac{DL}{LE} \):
\[ \frac{DL}{LE} = \frac{4}{\frac{4}{3}} = 4 \times \frac{3}{4} = 3 \]
- Calculate \( \frac{DM}{MF} \):
\[ \frac{DM}{MF} = \frac{6}{2} = 3 \]

5. **Compare the Ratios:**
- We find that:
\[ \frac{DL}{LE} = 3 \quad \text{and} \quad \frac{DM}{MF} = 3 \]
- Since both ratios are equal, we conclude that:
\[ \frac{DL}{LE} = \frac{DM}{MF} \]

6. **Conclusion:**
- By the Basic Proportionality Theorem, since the ratios are equal, we can conclude that line segment LM is parallel to line segment EF.

### Final Answer:
Yes, LM is parallel to EF.