Question

if two triangles are similar, their corresponding angles are: a. equal b. proportional c. different d. supplementary in △abc ∼ △def, ab = 10, ac = 15, and de = 5. what is the length of df? a. 20 b. 12 c. 10 d. 7.5

Explanation:

Step1: Recall property of similar triangles for first - question

By definition, if two triangles are similar, their corresponding angles are equal.

Step2: Use similarity ratio for second - question

Since $\triangle ABC\sim\triangle DEF$, the ratios of corresponding sides are equal, i.e., $\frac{AB}{DE}=\frac{AC}{DF}$. Substitute $AB = 10$, $AC = 15$, and $DE = 5$ into the proportion: $\frac{10}{5}=\frac{15}{DF}$. Cross - multiply gives $10\times DF=15\times5$, so $10DF = 75$, and $DF=\frac{75}{10}=7.5$.

Answer:

1. a. Equal
2. d. 7.5