Question

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

∠p ≅ ∠t

overline{pi} ≅ overline{at}

overline{ca} ≅ overline{gp}

∠c ≅ ∠g

Explanation:

Step1: Recall the property of similar polygons

Similar polygons have corresponding angles congruent.

Step2: Identify corresponding angles

In similar polygons, the angles with the same marking (in this case, the double - arc marking) are corresponding. In Figure 1, $\angle C$ has a double - arc marking, and in Figure 2, $\angle G$ has a double - arc marking. So, $\angle C$ and $\angle G$ are corresponding angles of the similar polygons.
Since similar polygons have corresponding angles congruent, $\angle C\cong\angle G$.

For the other options:

• $\angle P$ and $\angle T$: There is no indication (such as same arc markings) that they are corresponding angles.
• $\overline{PI}$ and $\overline{AT}$: They are not corresponding sides (the ratio of side lengths of similar polygons is constant, but these are not in the correct proportion relationship as corresponding sides).
• $\overline{CA}$ and $\overline{GP}$: They are not corresponding sides (again, no proportion relationship based on the side lengths of the similar polygons).

Answer:

$\angle C\cong\angle G$