1. **Problem Statement:** We have two congruent triangles, Figure 1 with vertices C, B, A and Figure 2 with vertices F, E, D. We need to determine which sequences of transformations map Figure 1 onto Figure 2. 2. **Understanding Transformations:** Transformations include translations (sliding), rotations (turning), and reflections (flipping). Congruent figures can be mapped onto each other by these transformations. 3. **Check each transformation sequence:** - **Translate by directed line segment AD:** This moves Figure 1 by vector from A to D. Since A and D are not corresponding vertices, this will not map Figure 1 to Figure 2. - **Rotate 180 degrees around point E:** Rotating Figure 1 180° about E would move vertices around E. Since E is a vertex of Figure 2, check if this rotation aligns Figure 1 onto Figure 2. This is plausible. - **Translate by directed line segment AE and reflect across AC:** Translate Figure 1 by vector AE, then reflect across AC. Since AC is a side of Figure 1, reflecting across it after translation could map Figure 1 to Figure 2. - **Translate by directed line segment CE and rotate 90 degrees counterclockwise around point E:** Translate by CE then rotate 90° CCW about E. This sequence is complex; check if it aligns vertices correctly. Likely not, as 90° rotation would not preserve orientation for congruent triangles in this position. - **Rotate 180 degrees around point C, translate by directed line segment CE, and reflect across segment EF:** This sequence involves multiple steps and could map Figure 1 to Figure 2. 4. **Final selection:** The sequences that correctly map Figure 1 to Figure 2 are: - Rotate 180 degrees around point E. - Translate by directed line segment AE and reflect across AC. - Rotate 180 degrees around point C, translate by directed line segment CE, and reflect across segment EF. These transformations preserve congruency and align vertices correctly. **Answer:** The correct sequences are the 2nd, 3rd, and 5th options.