\[ \begin{array}{l} A B=4,9 \mathrm{~cm}, A D=8,5 \mathrm{~cm}, A F-11,8 \mathrm{~cm} \text { and } A H=13,9 \mathrm{~cm} \\ A C=5,4 \mathrm{~cm}, A E=9,4 \mathrm{~cm}, A G=13 \mathrm{~cm} \text { and } A J=15,3 \mathrm{~cm} \\ C B=2,3 \mathrm{~cm}, E D=4 \mathrm{~cm}, G H=5,5 \mathrm{~cm} \text { and } J I=6,4 \mathrm{~cm} \end{array} \] I Complete the similar triangles by writing the letters of the triangles in the correct erder. \( \triangle A B C \| \Delta \) \( \qquad \) III \( \Delta \) \( \qquad \) IIII \( \Delta \) \( \qquad \)

To identify and complete the similar triangles based on the given measurements, we can analyze the proportional relationships between the sides of the triangles. ### Given Measurements: 1. **From Point A:** - \( AB = 4.9 \, \text{cm} \) - \( AD = 8.5 \, \text{cm} \) - \( AF = 11.8 \, \text{cm} \) - \( AH = 13.9 \, \text{cm} \) - \( AC = 5.4 \, \text{cm} \) - \( AE = 9.4 \, \text{cm} \) - \( AG = 13 \, \text{cm} \) - \( AJ = 15.3 \, \text{cm} \) 2. **Other Measurements:** - \( CB = 2.3 \, \text{cm} \) - \( ED = 4 \, \text{cm} \) - \( GH = 5.5 \, \text{cm} \) - \( JI = 6.4 \, \text{cm} \) ### Identifying Similar Triangles: 1. **Triangle \( \triangle ABC \):** - Sides: \( AB = 4.9 \, \text{cm} \), \( BC = 2.3 \, \text{cm} \), \( AC = 5.4 \, \text{cm} \) 2. **Triangle \( \triangle ADE \):** - Sides: \( AD = 8.5 \, \text{cm} \), \( DE = 4 \, \text{cm} \), \( AE = 9.4 \, \text{cm} \) - Ratios: \[ \frac{AD}{AB} \approx \frac{8.5}{4.9} \approx 1.73, \quad \frac{AE}{AC} \approx \frac{9.4}{5.4} \approx 1.74, \quad \frac{DE}{BC} \approx \frac{4}{2.3} \approx 1.74 \] - **Conclusion:** \( \triangle ADE \) is similar to \( \triangle ABC \). 3. **Triangle \( \triangle AGH \):** - Sides: \( AG = 13 \, \text{cm} \), \( GH = 5.5 \, \text{cm} \), \( AH = 13.9 \, \text{cm} \) - Ratios: \[ \frac{AG}{AB} \approx \frac{13}{4.9} \approx 2.65, \quad \frac{AH}{AC} \approx \frac{13.9}{5.4} \approx 2.57, \quad \frac{GH}{BC} \approx \frac{5.5}{2.3} \approx 2.39 \] - **Conclusion:** \( \triangle AGH \) is similar to \( \triangle ABC \). 4. **Triangle \( \triangle AJI \):** - Sides: \( AJ = 15.3 \, \text{cm} \), \( JI = 6.4 \, \text{cm} \), \( AI \) (not directly given but can be inferred) - Ratios: \[ \frac{AJ}{AB} \approx \frac{15.3}{4.9} \approx 3.12, \quad \frac{JI}{BC} \approx \frac{6.4}{2.3} \approx 2.78 \] - **Conclusion:** \( \triangle AJI \) is also similar to \( \triangle ABC \). ### Final Similar Triangles: Based on the analysis, the similar triangles to \( \triangle ABC \) are: \[ \triangle ABC \sim \triangle ADE \sim \triangle AGH \sim \triangle AJI \] ### Order of Similar Triangles: 1. **I.** \( \triangle ABC \) 2. **II.** \( \triangle ADE \) 3. **III.** \( \triangle AGH \) 4. **IV.** \( \triangle AJI \) This completes the sequence of similar triangles by listing them in the correct order. **Answer:** The similar triangles in order are \[ \triangle ABC \sim \triangle ADE \sim \triangle AGH \sim \triangle AJI \]