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 ∠A≅∠D angle upper A congruent to angle upper D BC ¯¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ Modifying above upper B upper C with bar congruent to Modifying above upper B upper C with bar AB ¯¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ Modifying above upper A upper B with bar congruent to Modifying above upper B upper D with bar AC ¯¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯

Answer 1

To prove that \( \triangle ABC \cong \triangle DBC \) using the ASA (Angle-Side-Angle) Congruence Theorem, we need to establish two angles and the included side being congruent between the two triangles.

Given:

• You probably already have \( \angle ABC \) congruent to \( \angle DBC \) (as these angles are commonly formed sharing the same vertex and line BC).

To apply the ASA theorem, we need to ensure the following information is stated:

1. Mark \( \angle A \) congruent to \( \angle D \): This ensures we have two angles, \( \angle A \) and \( \angle D \).
2. State that \( \overline{BC} \) is congruent to \( \overline{BC} \): This is the statement of the included side that both triangles share.

Thus, the additional pieces of information needed are:

• \( \angle A \cong \angle D \)
• \( \overline{BC} \cong \overline{BC} \) (common side)

With this information, you can apply the ASA theorem to conclude that \( \triangle ABC \cong \triangle DBC \).