In △ABC and △DEF , ∠A ≅ ∠D and ∠B ≅ ∠E . What additional information is needed to prove that △ABC ≅ △DEF by the ASA Congruence Theorem?(1 point) Responses BC¯¯¯¯¯¯¯¯ ≅ EF¯¯¯¯¯¯¯¯ BC¯¯¯¯¯¯¯¯ ≅ EF¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯ ≅ DE¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯ ≅ DE¯¯¯¯¯¯¯¯ ∠C ≅ ∠F ∠C ≅ ∠F AC¯¯¯¯¯¯¯¯ ≅ DF¯¯¯¯¯¯¯¯

Answer 1

To prove that triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent by the ASA (Angle-Side-Angle) Congruence Theorem, you already have two angles that are congruent: \( \angle A \cong \angle D \) and \( \angle B \cong \angle E \).

The ASA theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Therefore, the additional information you need is the congruence of the sides between the two triangles. Since you have the angles \( \angle A \) and \( \angle B \) congruent, you need the side that is included between those two angles.

The appropriate additional information to satisfy the ASA theorem is:

\( AB \cong DE \) (the side included between \( \angle A \) and \( \angle B \) in triangle \( ABC \) should be congruent to the side included between \( \angle D \) and \( \angle E \) in triangle \( DEF \)).

So the correct response is:

\( AB \cong DE \).