The image contains a geometric problem with a triangle labeled $\triangle BDH$, along with several other points labeled $A, C, E, F, G, H, K$, and a request to fill in information related to medians and other segments in the triangle.

The question is in Latvian and appears to ask for:

1. Identifying the medians of $\triangle BDH$.
2. A segment that is parallel to the median.
3. A special point, likely the centroid (since medians are mentioned), on segment $BD$.

Here's the approach to solving this:

1. Median of a triangle: A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. So, you need to determine which of the line segments in $\triangle BDH$ connects a vertex (likely $B$, $D$, or $H$) to the midpoint of the opposite side.

2. Medians of $\triangle BDH$:

   • Segment $HK$ could be a median, as it appears to divide side $BD$ into two equal parts at $K$.
   • Segment $BG$ might also be a median, dividing the side $DH$ into two equal parts at $G$.

3. Parallel segment: A segment parallel to the median would be one that maintains the same slope or direction as one of the medians but could be part of another triangle formed within the larger triangle, such as segment $EF$, which seems to be parallel to $HK$.

4. Special point (centroid): The centroid is the intersection point of the medians. If the problem asks for a point that lies on $BD$, it could be point $K$, which is the midpoint of $BD$.

Would you like more details on these steps or clarifications?

Follow-up Questions:

1. What exactly defines a median in a triangle, and how do we calculate its length?
2. What is the significance of the centroid in a triangle?
3. Could the centroid be outside of the triangle, or does it always lie inside?
4. How can we prove that a certain line segment is parallel to the median?
5. What role does symmetry play in solving this geometric problem?

Tip:

In any triangle, the centroid divides each median into a ratio of 2:1, with the longer part being closer to the vertex.