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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≅△DAO
triangle upper A upper C upper D congruent to triangle upper C upper A upper B

△DAB≅△CBA
triangle upper A upper O upper B congruent to triangle upper D upper O upper C

△DAB≅△DOC
triangle upper A upper O upper D congruent to triangle upper C upper O upper B
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Answer 1

In the proof that the diagonals of rectangle ABCD are congruent, after the statements that \( AD \cong BC \), \( AB \cong AB \), and \( \angle DAB \cong \angle CBA \), the next logical step would be to state congruent triangles that include the intersection point O.

The correct response is:

△DAB≅△CBA triangle upper A upper O upper B congruent to triangle upper D upper O upper C

This statement indicates that triangles AOB and DOC are congruent, which is necessary to use the triangle congruence criteria (such as the Angle-Side-Angle postulate) to show that the diagonals are congruent.