Question

if $\triangle def \cong \triangle uvw$, what are the corresponding parts? select all that apply.
$\overline{de} \cong \overline{uv}$ (checked)
$\overline{df} \cong \overline{uw}$ (checked)
$\angle d \cong \angle u$ (checked)
$\overline{fe} \cong \overline{wv}$ (checked)

Explanation:

When two triangles are congruent (denoted by $\cong$), their corresponding sides and angles are congruent. The order of the vertices in the congruence statement $\triangle DEF \cong \triangle UVW$ tells us the correspondence: $D$ corresponds to $U$, $E$ corresponds to $V$, and $F$ corresponds to $W$.

• For sides: Corresponding sides are named by the corresponding vertices. So $\overline{DE}$ (between $D$ and $E$) corresponds to $\overline{UV}$ (between $U$ and $V$), $\overline{DF}$ (between $D$ and $F$) corresponds to $\overline{UW}$ (between $U$ and $W$), and $\overline{FE}$ (between $F$ and $E$) corresponds to $\overline{WV}$ (between $W$ and $V$).
• For angles: $\angle D$ (at vertex $D$) corresponds to $\angle U$ (at vertex $U$).

All the selected options follow this correspondence, so they are correct.

Answer:

A. $\overline{DE} \cong \overline{UV}$ (correct), B. $\overline{DF} \cong \overline{UW}$ (correct), C. $\angle D \cong \angle U$ (correct), D. $\overline{FE} \cong \overline{WV}$ (correct)

(Note: Assuming the options are labeled A, B, C, D for the four checkboxes in order. If the original options had different labels, adjust accordingly, but based on the checkmarks, all these corresponding parts are correct due to the congruence of $\triangle DEF$ and $\triangle UVW$.)