Question

given the similar polygons in the image, which statement is true?
∠e ≅ ∠k
∠d ≅ ∠k
overline{fg} ≅ overline{ab}
overline{gh} ≅ overline{bc}

Explanation:

Step1: Recall the property of similar polygons

Similar polygons have corresponding angles congruent and corresponding sides proportional.

Step2: Analyze each option

• For $\angle E\cong\angle K$: In similar polygons, $\angle E$ should correspond to $\angle F$ (not $\angle K$), so this is false.
• For $\angle D\cong\angle K$: Since the polygons are similar, and by the order of the polygons (assuming proper correspondence), $\angle D$ and $\angle K$ are corresponding angles. Corresponding angles of similar polygons are congruent, so this is true.
• For $\overline{FG}\cong\overline{AB}$: $\overline{FG}=3y + 0.15$ and $\overline{AB} = 2.5$. Since the sides of similar polygons are proportional ($\frac{FG}{AB}=\frac{FK}{AE}$ etc., and $FG

eq AB$ as per side - length values), this is false.

• For $\overline{GH}\cong\overline{BC}$: $\overline{GH}=8x + 0.45$ and $\overline{BC}=3.5$. Since the sides of similar polygons are proportional ($\frac{GH}{BC}=\frac{GJ}{CD}$ etc., and $GH

eq BC$ as per side - length values), this is false.

Answer:

$\angle D\cong\angle K$