Based on the markings in the diagram, what additional information must be stated in order to prove △ABC≅△DBC by the ASA Congruence Theorem?

Question

(1 point)
Responses

∠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¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper B upper C with bar

AC ¯¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯

Answer 1

To use the ASA (Angle-Side-Angle) Congruence Theorem to prove that triangles \( \triangle ABC \) and \( \triangle DBC \) are congruent, you need two angles and the included side to be congruent between the two triangles.

In this case, you already have:

1. An angle \( \angle ABC \) which is common to both triangles,
2. You need another angle and the included side to establish the congruence.

Out of the options provided, stating that \( \angle A \cong \angle D \) gives you the second angle required to apply the ASA Theorem because \( AB \) is the included side between these two angles in their respective triangles.

So the additional information needed is:

∠A ≅ ∠D