Question

1. find sides d and e.

Explanation:

Step1: Set up proportion for parallel lines

When two transversals cut parallel lines, the corresponding segments are proportional. For side $d$:
$\frac{6}{d} = \frac{8}{5}$

Step2: Solve for $d$

Cross-multiply to isolate $d$:
$8d = 6 \times 5$
$d = \frac{30}{8} = \frac{15}{4} = 3.75$

Step3: Set up proportion for $e$

Use the proportionality rule for side $e$:
$\frac{8}{e} = \frac{6}{2}$

Step4: Solve for $e$

Cross-multiply to isolate $e$:
$6e = 8 \times 2$
$e = \frac{16}{6} = \frac{8}{3} \approx 2.67$

Answer:

$d = \frac{15}{4}$ (or 3.75), $e = \frac{8}{3}$ (or approximately 2.67)