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
∠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
BC ¯¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper B upper C with bar
AB ¯¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯
by the ASA Congruence Theorem?
(1 point)
Responses
∠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
BC ¯¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
Modifying above upper B upper C with bar congruent to Modifying above upper B upper C with bar
AB ¯¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯
Answers
GPT-4o mini
To prove \( \triangle ABC \cong \triangle DBC \) by the ASA (Angle-Side-Angle) Congruence Theorem, we need to establish that two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle.
From the markings in the diagram, we have:
1. One angle is \( \angle ABC \) which is common to both triangles \( \triangle ABC \) and \( \triangle DBC \).
2. We need another pair of congruent angles and the included side between those angles.
To satisfy the ASA congruence criterion, we can derive that we need to specify one of the following:
- \( \angle A \cong \angle D \) (This gives the second angle).
- \( AC \cong DC \) (This gives the included side which is between the angles).
- The lengths of sides \( AB \) and \( BD \) are also congruent (This would provide a side connecting the two angles clearly but is not directly applicable in standard ASA form).
Thus, the best response to provide enough information would be:
**\( \angle A \cong \angle D \)**
This statement provides the necessary angle congruence needed to complete the ASA requirement, as it shows both triangles have two angles (one being common and the second specified) and the included side (the common side \( BC \)).
From the markings in the diagram, we have:
1. One angle is \( \angle ABC \) which is common to both triangles \( \triangle ABC \) and \( \triangle DBC \).
2. We need another pair of congruent angles and the included side between those angles.
To satisfy the ASA congruence criterion, we can derive that we need to specify one of the following:
- \( \angle A \cong \angle D \) (This gives the second angle).
- \( AC \cong DC \) (This gives the included side which is between the angles).
- The lengths of sides \( AB \) and \( BD \) are also congruent (This would provide a side connecting the two angles clearly but is not directly applicable in standard ASA form).
Thus, the best response to provide enough information would be:
**\( \angle A \cong \angle D \)**
This statement provides the necessary angle congruence needed to complete the ASA requirement, as it shows both triangles have two angles (one being common and the second specified) and the included side (the common side \( BC \)).