Question

1. given that △abc ~ △def, ab : de = 3 : 1, ac = 6, then df is _. a. 18 b. 2 c. 54 d. $\frac{2}{3}$ 2. the following two triangles are similar to each other, m = _. a. 1 b. 2 c. 3 d. 4

Explanation:

Step1: Recall property of similar - triangles

For similar triangles $\triangle ABC\sim\triangle DEF$, the ratios of corresponding sides are equal, i.e., $\frac{AB}{DE}=\frac{AC}{DF}$.

Step2: Substitute given values

We know that $\frac{AB}{DE} = 3:1=3$ and $AC = 6$. Substituting into $\frac{AB}{DE}=\frac{AC}{DF}$, we get $3=\frac{6}{DF}$.

Step3: Solve for $DF$

Cross - multiply: $3\times DF=6$, then $DF = 2$.

Step1: Identify corresponding sides of similar triangles

For two similar triangles, the ratios of corresponding sides are equal. The ratio of the sides of the larger triangle to the smaller triangle is $\frac{6}{3}=\frac{4}{2}=2$.

Step2: Set up proportion to find $m$

We have $\frac{8}{m}=2$.

Step3: Solve for $m$

Cross - multiply: $8 = 2m$, then $m = 4$.

Answer:

B. 2