27. given: $ \triangle bat \cong \triangle cat $ which statement is true by cpctc? $ \angle tac \cong \angle bta $ $ \overline{bt} \cong \overline{ta} $ $ \angle bat \cong \angle cat $ $ \overline{ct} \cong \overline{at} $

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# Brief Explanations:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent". When $\triangle BAT\cong\triangle CAT$, we look at the corresponding parts.
- For $\angle TAC$ and $\angle BTA$: These are not corresponding angles of $\triangle BAT$ and $\triangle CAT$.
- For $\overline{BT}\cong\overline{TA}$: $\overline{BT}$ corresponds to $\overline{CT}$ (not $\overline{TA}$) in $\triangle CAT$ since $\triangle BAT\cong\triangle CAT$.
- For $\angle BAT\cong\angle CAT$: Since $\triangle BAT\cong\triangle CAT$, by CPCTC, the corresponding angles $\angle BAT$ and $\angle CAT$ (where $\angle BAT$ in $\triangle BAT$ and $\angle CAT$ in $\triangle CAT$) are congruent.
- For $\overline{CT}\cong\overline{AT}$: $\overline{CT}$ corresponds to $\overline{BT}$ (not $\overline{AT}$)  as $\triangle BAT\cong\triangle CAT$.

# Answer:
$\angle BAT\cong\angle CAT$

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