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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≅△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

△DAB≅△DOC

Answer 1

In the context of proving the congruence of the diagonals of rectangle ABCD, after stating that \(AD \cong BC\), \(AB \cong AB\), and \(\angle DAB \cong \angle CBA\), the next logical step is to apply the Side-Angle-Side (SAS) congruence postulate.

The correct statement that follows is:

\(\triangle DAB \cong \triangle CBA\)

This is because \(AD\) is congruent to \(BC\), \(AB\) is congruent to itself, and the angles are congruent, fulfilling the conditions of the SAS criterion for triangle congruence.

Therefore, the correct response is:

• △DAB≅△CBA