1. **State the problem:** We are given two trapezoids with side lengths and asked to verify if they are similar. 2. **Recall the similarity rule for trapezoids:** Two trapezoids are similar if their corresponding sides are proportional. 3. **List the sides of the smaller trapezoid:** Top = 5, Left = 15, Right = 7, Bottom = 6. 4. **List the sides of the larger trapezoid:** Top = 10, Left = 30, Right = 14, Bottom = 12. 5. **Calculate the ratios of corresponding sides:** - Top sides ratio: $$\frac{10}{5} = 2$$ - Left sides ratio: $$\frac{30}{15} = 2$$ - Right sides ratio: $$\frac{14}{7} = 2$$ - Bottom sides ratio: $$\frac{12}{6} = 2$$ 6. **Interpret the results:** All corresponding side ratios are equal to 2, which means the sides are proportional. 7. **Conclusion:** Since all corresponding sides have the same ratio, the trapezoids are similar by definition. **Final answer:** The trapezoids are similar because their corresponding sides are proportional with ratio 2.