1. **Problem statement:** Given a triangle with points A, B, C, D, E on one side such that $AB=BC=CD=DE$ and the segment $BI=2$ cm. We need to find the length of $EF$. 2. **Understanding the problem:** Since $AB=BC=CD=DE$, the side is divided into 4 equal segments. The segments $BI$, $CH$, $DG$, and $EF$ are horizontal lines inside the triangle corresponding to these divisions. 3. **Key idea:** The horizontal segments inside the triangle decrease proportionally as we move down from the top vertex A to the base. Since $BI=2$ cm corresponds to the first segment, and the segments are proportional to the distances from A, the length of $EF$ (the bottom segment) will be 4 times $BI$ because $EF$ corresponds to the full base segment. 4. **Calculation:** Since $BI=2$ cm and $EF$ corresponds to the full base segment, $$EF=4 \times BI=4 \times 2=8$$ 5. **Answer:** The length of $EF$ is 8.