Based on the diagram, what additional information must be stated in order to prove △ABD ≅ △DBC by the ASA Congruence Theorem? (1 point) Responses ∠A≅∠D ∠A≅∠D AB¯¯¯¯¯¯¯¯ ≅ BD¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯ ≅ BD¯¯¯¯¯¯¯¯ BC¯¯¯¯¯¯¯¯ ≅ BC¯¯¯¯¯¯¯¯ BC¯¯¯¯¯¯¯¯ ≅ BC¯¯¯¯¯¯¯¯ AC¯¯¯¯¯¯¯¯ ≅ DC¯¯¯¯¯¯¯¯

Answer 1

To prove that triangles \( \triangle ABD \) and \( \triangle DBC \) are congruent by the ASA (Angle-Side-Angle) Congruence Theorem, you must establish two angles and the included side being congruent in each triangle.

Assuming that \( \angle A \) and \( \angle D \) are the angles at vertices A and D, respectively, and that \( AB \) and \( BD \) are the sides connecting those angles, we can summarize the required information:

1. You need to show that \( \angle A \cong \angle D \) (as one of the angles) and
2. You need to show that the side connecting those angles, \( \overline{AB} \) or \( \overline{BD} \), is congruent.

Therefore, based on the responses provided, the additional information required would be:

• \( \angle A \cong \angle D \) (you need to establish the congruence of these angles).

So the correct option is:

\( \angle A \cong \angle D \).