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13 of 1313 of 13 Items Question Based on the diagram, what additional information must be stated in order to prove △ABD ≅ △DBC by the ASA Congruence Theorem? (1 point) Responses AB¯¯¯¯¯¯¯¯ ≅ BD¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯ ≅ BD¯¯¯¯¯¯¯¯ BC¯¯¯¯¯¯¯¯ ≅ BC¯¯¯¯¯¯¯¯ BC¯¯¯¯¯¯¯¯ ≅ BC¯¯¯¯¯¯¯¯ ∠A≅∠D ∠A≅∠D AC¯¯¯¯¯¯¯¯ ≅ DC¯¯¯¯¯¯¯¯ AC¯¯¯¯¯¯¯¯ ≅ DC¯¯¯¯¯¯¯¯ Skip to navigation

3 answers

To prove that triangles \( \triangle ABD \) and \( \triangle DBC \) are congruent by the ASA (Angle-Side-Angle) Congruence Theorem, you need to establish two angles and the included side between those angles in each triangle.

Assuming that:

  • You already have one angle from each triangle: \( \angle A \) from \( \triangle ABD \) and \( \angle D \) from \( \triangle DBC \),
  • You also have the side \( AB \) which is shared between the two triangles,

you would require one additional piece of information, which would be a second angle in either triangle.

Therefore, the correct response from the options provided would likely be:

\( \angle A \cong \angle D \)

This would establish that you have the included side (AB) and the two angles (∠A and ∠D), satisfying the criteria for the ASA theorem.

you were wrong

I apologize for the confusion. Let's clarify the requirements for proving that \( \triangle ABD \cong \triangle DBC \) using the ASA (Angle-Side-Angle) Congruence Theorem.

To use the ASA theorem, you need to have:

  1. Two angles in one triangle congruent to two angles in the other triangle.
  2. The included side between those two angles must also be congruent.

From the setup:

  • \( AB \) and \( BD \) could be the corresponding sides shared or not shared by the two triangles.
  • We require information about two angles.

If, in fact, you have established one angle already and need one additional piece of information to establish ASA, you would typically need one of the following:

  • The angle between the two sides (like \( \angle A \) or \( \angle D \)), or
  • Another pair of angles (like \( \angle ABD \) and \( \angle DBC \)).

Given the responses you provided, the correct choice for additional information needed to prove \( \triangle ABD \cong \triangle DBC \) using the ASA theorem will depend on what has already been given, but could be one of the congruencies involving angles or sides that helps establish the congruence.

If you could specify what you currently have in terms of already known angles or sides, I would be glad to help further narrow down the necessary additional information! Thank you for your patience.