Question

1. use the diagram below to answer parts i, ii, and iii. triangle abc is similar to triangle def. (i) what is the length of ab? a 2 cm b 3 1/3 cm c 4 cm d 4 1/3 cm

Explanation:

Step1: Identify corresponding sides

For similar triangles $\triangle ABC$ and $\triangle DEF$, if we assume the side - length ratio is based on the given sides. Let's assume the ratio of corresponding sides is the same.

Step2: Set up the proportion

Let the side of length $4$ cm in $\triangle ABC$ correspond to the side of length $8$ cm in $\triangle DEF$, and the side of length $x$ in $\triangle ABC$ correspond to the side of length $16$ cm in $\triangle DEF$. The ratio of the sides of similar triangles is constant. So, $\frac{4}{8}=\frac{x}{16}$.

Step3: Solve the proportion

Cross - multiply: $8x = 4\times16$. Then $8x=64$, and $x = 8$ cm.

Answer:

$8$ cm