Two congruent triangles, upper A upper B upper C and upper B upper C upper D, are mirrored over side upper B upper C on a plane. B both angels B are congruent. Both angels C are congruent.

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

BC ¯¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper B upper C with bar

∠A≅∠D
angle upper A congruent to angle upper D

AC ¯¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯
Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar

AB ¯¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯

Answer 1

To prove △ABC ≅ △DBC by the ASA (Angle-Side-Angle) Congruence Theorem, you need to establish two angles and the included side between them as congruent in both triangles.

From the information given:

• ∠B is common to both triangles (since both triangles share the side BC and angle B).
• You have noted that both angles C are congruent (so ∠C in triangle ABC and ∠C in triangle DBC are equal).

To apply the ASA theorem, you still need to demonstrate the congruence of the sides that are between the two pairs of angles. The side between angles A and C in triangle ABC is AC, and the side between angles D and C in triangle DBC is DC.

Thus, the additional information that must be stated to prove the congruence using the ASA theorem is:

AC ¯¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯

This establishes that the two triangles have two angles (∠A ≅ ∠D and ∠C ≅ ∠C) and the included side (AC ≅ DC) congruent, affirming that △ABC ≅ △DBC.