Use the image to answer the question. Based on the markings in the diagram, what additional information must be stated in order to prove △ABC≅△DBC by the ASA Congruence Theorem? (1 point) Responses AC ¯¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar ∠A≅∠D angle upper A congruent to angle upper D AB ¯¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper B upper D with bar BC ¯¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯

Answer 1

To prove that triangle \( \triangle ABC \) is congruent to triangle \( \triangle DBC \) by the ASA (Angle-Side-Angle) Congruence Theorem, we need to have two angles and the included side between them.

Given the information you provided about the markings in the diagram, the additional information that must be established to use the ASA theorem would be the congruence of one pair of angles and the congruence of the side that is included between those angles.

From the options you provided, the response that directly corresponds to this requirement is:

∠A ≅ ∠D

This establishes that the corresponding angles are congruent, which, along with knowing that the sides (like \( BC \)) are common to both triangles, would enable us to use the ASA theorem to conclude that \( \triangle ABC \cong \triangle DBC \).