1. The problem asks to identify sequences of transformations that show triangles ABC and AED are similar, given AC = 6 units. 2. Similar triangles can be shown by transformations such as dilation (scaling), reflection, translation, or combinations that map one triangle onto the other while preserving shape but not necessarily size. 3. Given lengths: AB = 8, BC = 4, AC = 6, AE = 3, ED = 2, DE = 4. 4. Notice that AE = 3 is half of AC = 6, and ED = 2 is half of BC = 4, so triangle AED is a scaled-down version of ABC by a factor of 1/2 centered at A. 5. To show similarity, we can dilate triangle ABC by scale factor 1/2 centered at A to get triangle AED. 6. After dilation, a reflection over line AC may be needed to align the triangles properly. 7. Now, analyze each option: - A: Dilate ABC by 1/2 at A, then reflect over AC. This matches the reasoning. - B: Dilate AED by 2 at A, then reflect over AC. This is the reverse of A and also valid. - C: Reflect ABC over AC, then dilate by 1/2 at A. Reflection first then dilation also works. - D: Reflect AED over AC, then dilate by 2 at A. Reverse of C, also valid. - E: Translate AED by DC, then dilate by 2 at C. This changes center and scale factor, not matching similarity centered at A. - F: Translate either triangle by DC, then reflect over AC. Translation alone does not preserve similarity unless combined with correct dilation. 8. Therefore, correct sequences are A, B, C, and D. Final answer: A, B, C, and D.