Question

in the diagram below, $\angle ghf \cong \angle def$. if $gh = 4$, $fe = 6$, $df = 4$, and $fh = 4.8$, find the length of $\overline{de}$. figures are not necessarily drawn to scale.
answer
attempt 1 out of 2
$de = \square$
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Explanation:

Step1: Identify similar triangles

$\angle GHF \cong \angle DEF$, and $\angle HFG = \angle EFD$ (vertical angles). Thus, $\triangle GHF \sim \triangle DEF$ by AA similarity.

Step2: Set up proportion of sides

Corresponding sides are proportional: $\frac{GH}{DE} = \frac{FH}{FE}$

Step3: Substitute given values

$\frac{4}{DE} = \frac{4.8}{6}$

Step4: Solve for $DE$

Cross-multiply: $4.8 \times DE = 4 \times 6$
$DE = \frac{24}{4.8}$

Answer:

$5$