Question

given the similar polygons in the image, which statement is true?

∠e ≅ ∠k

∠d ≅ ∠k

overline{gh} ≅ overline{bc}

overline{fg} ≅ overline{ab}

Explanation:

Step1: Recall the property of similar polygons

Similar polygons have corresponding angles congruent and corresponding sides proportional.

Step2: Identify corresponding angles

In similar polygons, \(\angle D\) in Figure 2 corresponds to \(\angle K\) in Figure 1. So, \(\angle D\cong\angle K\).
For \(\angle E\), it corresponds to \(\angle F\) (not \(\angle K\)).
For sides: \(\overline{GH}\) corresponds to \(\overline{AB}\) (\(\frac{GH}{AB}=\frac{3}{2.5} = 1.2\)), \(\overline{FG}\) corresponds to \(\overline{ED}\) (\(\frac{FG}{ED}=\frac{3y + 0.15}{2.2}\), and \(\overline{BC}\) has length \(3.5\), \(\overline{GH}\) has length \(3\) so \(\overline{GH}
ot\cong\overline{BC}\), \(\overline{FG}\) has length \(3y+0.15\) and \(\overline{AB}\) has length \(2.5\) so \(\overline{FG}
ot\cong\overline{AB}\).

Answer:

\(\angle D\cong\angle K\)