1. **Problem Statement:** We are given a right triangle \(\triangle DFG\) with \(FE\) perpendicular to the hypotenuse \(DG\). We need to determine which triangles are similar to \(\triangle DEF\). 2. **Key Concept:** When a perpendicular is drawn from the right angle vertex to the hypotenuse in a right triangle, it creates two smaller right triangles that are similar to the original triangle and to each other. 3. **Triangles to consider:** \(\triangle DEF\), \(\triangle DFG\), \(\triangle EGF\), \(\triangle FEG\), and \(\triangle GDF\). 4. **Similarity Reasoning:** - \(\triangle DEF\) shares angle \(D\) with \(\triangle DFG\) and both have a right angle, so \(\triangle DEF \sim \triangle DFG\). - \(\triangle DEF\) shares angle \(E\) with \(\triangle EGF\) and both have a right angle, so \(\triangle DEF \sim \triangle EGF\). - \(\triangle FEG\) and \(\triangle GDF\) are not directly similar to \(\triangle DEF\) because they do not share the necessary angles or right angle positions. 5. **Conclusion:** The triangles similar to \(\triangle DEF\) are \(\triangle DFG\) and \(\triangle EGF\). **Final answer:** A. \(\triangle DFG\) and B. \(\triangle EGF\) are similar to \(\triangle DEF\).