Question
In a proof that the diagonals of rectangle ABCD are congruent, which statement comes just after the statements that AD¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ , AB¯¯¯¯¯¯¯¯≅AB¯¯¯¯¯¯¯¯ , and ∠DAB≅∠CBA ? (1 point) Responses △DAB≅△DAO triangle upper A upper C upper D congruent to triangle upper C upper A upper B △DAB≅△DOC triangle upper A upper O upper D congruent to triangle upper C upper O upper B △DAB≅△CBA triangle upper A upper O upper B congruent to triangle upper D upper O upper C △DAB≅△AOB
Answers
GPT-4o mini
In a proof that the diagonals of rectangle ABCD are congruent, after stating that \( AD \cong BC \), \( AB \cong AB \), and \( \angle DAB \cong \angle CBA \), the next logical statement to include would involve demonstrating the congruence of triangles formed by the diagonals.
The appropriate statement that follows would be:
**\(\triangle AOB \cong \triangle COD\)**
This statement establishes the congruence of the triangles formed by drawing the diagonals \( AC \) and \( BD \), which together demonstrate that the diagonals of rectangle ABCD are congruent.
So, if we consider the response options provided, the correct statement should represent that congruence. But since that isn't explicitly present in the response options you've given, the option that is most aligned with the structure of the proof would generally be expected in a correctly framed response regarding triangle correlations and congruences involving the defined angles and sides referenced.
Based on typical phrasing in such a proof, the confidence lies most in selecting **\(\triangle AOB \cong \triangle COD\)** if that option were available or structurally similar in logic.
If one of your options is specifically indicated as \(\triangle DAB \cong \triangle CBA\) it might represent a misalignment with norms of triangle naming but still is aiming at establishing congruence, verify that selection accordingly.
The appropriate statement that follows would be:
**\(\triangle AOB \cong \triangle COD\)**
This statement establishes the congruence of the triangles formed by drawing the diagonals \( AC \) and \( BD \), which together demonstrate that the diagonals of rectangle ABCD are congruent.
So, if we consider the response options provided, the correct statement should represent that congruence. But since that isn't explicitly present in the response options you've given, the option that is most aligned with the structure of the proof would generally be expected in a correctly framed response regarding triangle correlations and congruences involving the defined angles and sides referenced.
Based on typical phrasing in such a proof, the confidence lies most in selecting **\(\triangle AOB \cong \triangle COD\)** if that option were available or structurally similar in logic.
If one of your options is specifically indicated as \(\triangle DAB \cong \triangle CBA\) it might represent a misalignment with norms of triangle naming but still is aiming at establishing congruence, verify that selection accordingly.
Choose an option