The problem in the image involves a proportion relating segments in two triangles, which appear to be similar based on their corresponding angles. The equation given asks for the ratio of segments $\frac{KL}{LM}$ to be completed with the corresponding ratio from the other triangle.

Key Observations:

1. The two triangles (one with vertices $K, L, M$ and the other with $P, Q, O$) seem to have been drawn to suggest similarity, likely because their angles match.
2. Since similar triangles have proportional sides, we can match corresponding sides to set up a proportion.

Step-by-Step Solution:

• From the image, triangle $\triangle KLM$ and $\triangle POQ$ are the triangles in question.
• The segment $KL$ corresponds to $PO$, and $LM$ corresponds to $OQ$ (based on the positions of angles and how the triangles align).

Thus, the completed proportion should be:

$\frac{KL}{LM} = \frac{PO}{OQ}.$

Final Answer:

Fill in the blanks as: $\frac{KL}{LM} = \frac{PO}{OQ}.$

Would you like a deeper explanation or help solving a similar triangle problem? Let me know!

Related Questions:

1. How can you determine triangle similarity using angle-angle (AA) postulate?
2. Why are the ratios of corresponding sides in similar triangles always equal?
3. How can you use proportions in real-life scenarios like map scaling?
4. What are the criteria for congruence of two triangles?
5. Can similarity be proven using side-angle-side (SAS)?

Tip:

Always label corresponding sides clearly when working with similar triangles to avoid confusion while setting up proportions!