Question
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)
Responses
DA¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
by the Reflexive Property of Congruence.
Modifying above upper D upper A with bar congruent to Modifying above upper B upper C with bar by the Reflexive Property of Congruence.
AB¯¯¯¯¯¯¯¯≅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.
, 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)
Responses
DA¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯
by the Reflexive Property of Congruence.
Modifying above upper D upper A with bar congruent to Modifying above upper B upper C with bar by the Reflexive Property of Congruence.
AB¯¯¯¯¯¯¯¯≅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.
Answers
GPT-4o mini
To prove that triangles \( \triangle ABC \) and \( \triangle CDA \) are congruent by the ASA (Angle-Side-Angle) Congruence Theorem, we need the additional information that the sides \( DA \) and \( BC \) are congruent.
The correct choice for this information would thus be:
**DA̅̅̅̅̅≅BC̅̅̅̅̅ by the Reflexive Property of Congruence.**
This step confirms that the sides opposite the congruent angles (∠BCA ≅ ∠DAC and ∠BAC ≅ ∠DCA) in triangles ABC and CDA are equal, necessary for applying the ASA theorem.
The correct choice for this information would thus be:
**DA̅̅̅̅̅≅BC̅̅̅̅̅ by the Reflexive Property of Congruence.**
This step confirms that the sides opposite the congruent angles (∠BCA ≅ ∠DAC and ∠BAC ≅ ∠DCA) in triangles ABC and CDA are equal, necessary for applying the ASA theorem.