Question
Use the image to answer the question.
A quadrilateral upper A upper B upper C upper D. Two diagonals connect vertices upper A to upper C and upper B to upper D. The point of intersection is upper O.
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≅△AOB
triangle upper A upper D upper B congruent to triangle upper C upper B upper D
△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≅△DAO
triangle upper A upper C upper D congruent to triangle upper C upper A upper B
A quadrilateral upper A upper B upper C upper D. Two diagonals connect vertices upper A to upper C and upper B to upper D. The point of intersection is upper O.
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≅△AOB
triangle upper A upper D upper B congruent to triangle upper C upper B upper D
△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≅△DAO
triangle upper A upper C upper D congruent to triangle upper C upper A upper B
Answers
GPT-4o mini
In the context of proving that the diagonals of rectangle ABCD are congruent, based on the provided statements—AD≅BC, AB≅AB, and ∠DAB≅∠CBA—the next logical statement to include would be about triangles involving vertex O, the intersection of the diagonals.
Given the context, the correct statement that comes next is:
**△DAB≅△DOC**
Triangle AOD is congruent to triangle BOC.
This statement utilizes the Side-Angle-Side (SAS) postulate, as it confirms that two sides and the included angle of the triangles are congruent, leading to the conclusion that the diagonals are congruent.
Given the context, the correct statement that comes next is:
**△DAB≅△DOC**
Triangle AOD is congruent to triangle BOC.
This statement utilizes the Side-Angle-Side (SAS) postulate, as it confirms that two sides and the included angle of the triangles are congruent, leading to the conclusion that the diagonals are congruent.