Given that,
$$D$$ and $$E$$ are the midpoints of $$AB$$ and $$BC$$ respectively
$$DF || BC$$ and
$$AF =2.6\ cm$$
To prove: $$DBEF$$ is a parallelogram
To find: $$AC$$
Proof:
In $$\triangle ABC$$
$$D$$ is the mid point of $$AB$$ and $$DF \parallel BC$$
$$\Rightarrow F$$ is the mid point of $$AC$$ $$ ...(1)$$ [ Converse of mid point theorem]
Now, $$F$$ and $$E$$ are the mid point of $$AC$$ and $$BC$$
$$\Rightarrow EF \parallel AB$$ [ Mid point theorem]
$$\Rightarrow EF \parallel DB\qquad...(2)$$
Given,
$$DF \parallel BC\Rightarrow DF \parallel BE ....(3)$$
From equation $$(2)$$ and $$(3)$$,
$$DBEF$$ is a parallelogram.
Since, $$F$$ is the midpoint of $$AC$$
$$\therefore AC=2\times AF =2\times 2.6=5.2\ cm$$