Use the image to answer the question.Parallelogram upper A upper D upper C upper B is graphed on a plane, with diagonal upper A upper C.In parallelogram ABCD, diagonal AC¯¯¯¯¯¯¯¯ is drawn, and ∠BCA≅∠DAC and ∠BAC≅∠DCA . In order to prove △ABC≅△CDA by the ASA Congruence Theorem, what additional information must be stated and justified? (1 point)ResponsesAB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ by the Triangle Angle Sum Theorem.Modifying above upper A upper B with bar congruent to Modifying above upper C upper D with bar by the Triangle Angle Sum Theorem.AC¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ by the Reflexive Property of Congruence.Modifying above upper A upper C with bar congruent to Modifying above upper A upper C with bar by the Reflexive Property of Congruence.∠B≅∠D by the Reflexive Property of Congruence.angle upper B congruent to angle upper D by the Reflexive Property of Congruence.DA¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ by the Reflexive Property of Congruence.

Answer 1

To prove triangles \( \triangle ABC \cong \triangle CDA \) using the ASA (Angle-Side-Angle) Congruence Theorem, we must confirm that the included side between the two angles is congruent. Since we already have that \( \angle BCA \cong \angle DAC \) and \( \angle BAC \cong \angle DCA \), we just need to show the congruence of the side \( AC \).

The additional information needed and justified in this case is:

\( AC \cong AC \) by the Reflexive Property of Congruence.

This shows that the diagonal \( AC \) is the same length in both triangles, satisfying the requirements of the ASA theorem to conclude that \( \triangle ABC \cong \triangle CDA \).