Question

according to the diagram, which are congruent? check all that apply.
△abc and △def
△abc and △dfe
∠bac ≅ ∠def
∠acb ≅ ∠def
\overline{ab} and \overline{df}
\overline{ac} and \overline{df}

Explanation:

Step1: Analyze triangle congruence

For triangles, if their corresponding sides and angles are equal, they are congruent. In \(\triangle ABC\) and \(\triangle DFE\), \(BC = FE\) (marked with three lines), \(\angle B=\angle E\), \(\angle C=\angle F\). By ASA (Angle - Side - Angle) congruence criterion, \(\triangle ABC\cong\triangle DFE\). \(\triangle ABC\) and \(\triangle DEF\) do not have corresponding sides and angles in order for congruence.

Step2: Analyze angle congruence

\(\angle BAC\) is not congruent to \(\angle DEF\) as per the diagram. \(\angle ACB\) is not congruent to \(\angle DEF\) as per the diagram.

Step3: Analyze side congruence

\(\overline{AB}\) and \(\overline{DF}\): From the congruence \(\triangle ABC\cong\triangle DFE\), \(AB = DF\) (corresponding sides of congruent triangles). \(\overline{AC}\) and \(\overline{DF}\): \(AC\) is not equal to \(DF\) as per the side - marking in the diagram.

Answer:

\(\triangle ABC\) and \(\triangle DFE\), \(\overline{AB}\) and \(\overline{DF}\)