Question

if dgfe ≅ tuvw, what are the corresponding parts? select all that apply.
(overline{dg}congoverline{uv}) (angle fcongangle w) (angle econgangle u) (overline{gd}congoverline{ut})

Explanation:

Step1: Understand congruent polygons

When $DGFE\cong TUVW$, corresponding sides and angles are congruent.

Step2: Analyze side - correspondences

The order of vertices in the congruence statement gives side correspondences. $\overline{DG}$ corresponds to $\overline{UV}$ and $\overline{GD}$ (same segment as $\overline{DG}$ just named in reverse) corresponds to $\overline{UT}$.

Step3: Analyze angle - correspondences

For angles, $\angle F$ in $DGFE$ corresponds to $\angle W$ in $TUVW$. $\angle E$ does not correspond to $\angle U$; based on the order, $\angle E$ corresponds to $\angle V$. So $\angle E\cong\angle U$ is incorrect.

Answer:

1. $\overline{DG}\cong\overline{UV}$
2. $\angle F\cong\angle W$
3. $\overline{GD}\cong\overline{UT}$