Question

The ASA Congruence Theorem Quick Check
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Question
Use the image to answer the question.

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.

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

AB ¯¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯
Modifying above upper A upper B with bar congruent to Modifying above upper B upper D with bar

∠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

AC ¯¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯
Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar
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Answer 1

To prove △ABC ≅ △DBC using the ASA Congruence Theorem, you need two angles and the included side to be congruent between the two triangles.

You mentioned that both ∠B angles and both ∠C angles are already congruent, which indicates two of the necessary angles for the ASA theorem. The additional information required is to state that the sides between the two angles are congruent, specifically:

**AB ≅ BD**

This establishes that the sides opposite angles A and D are also equal, allowing you to conclude that the triangles are congruent using the ASA theorem. Thus, the correct response is:

**AB ¯¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯** (AB congruent to BD)