1. **State the problem:** Rachel wants to find the length of the lake by proving two triangles are similar and then using proportions. 2. **Identify given sides:** Left triangle sides: 53 m, 33 m, 15 m. Right triangle sides: 212 m, 60 m, unknown side. 3. **Check ratios of corresponding sides:** - Ratio of top sides: $\frac{212}{53} = 4$ - Ratio of bottom sides: $\frac{60}{15} = 4$ - Ratio of left sides: $\frac{?}{33}$ (unknown) 4. Since two pairs of corresponding sides have ratio 4:1, check if included angle is equal to use SAS similarity. 5. The triangles share the angle between these sides (the vertex where they intersect), so the included angle is the same. 6. By SAS similarity criterion, the triangles are similar because two sides are in proportion and the included angle is equal. 7. Use the ratio 4:1 to find the unknown side (length of the lake): $$\text{Length of lake} = 4 \times 33 = 132\text{ m}$$ **Final answer:** The triangles are similar by SAS similarity, and the length of the lake is 132 m.