To determine which statement comes just after the stated congruences in the proof that the diagonals of rectangle ABCD are congruent (specifically after the statements \(AD \cong BC\), \(AB \cong AB\), and \(\angle DAB \cong \angle CBA\)), we need to consider what has been established so far.
The established statements show that:
- The opposite sides of the rectangle are equal: \(AD \cong BC\) and \(AB \cong AB\).
- The angles formed at one vertex are congruent.
Next, you typically use the Side-Angle-Side (SAS) congruence criterion. Since we are looking at triangle congruences involving the diagonals, the correct subsequent statement should show that two triangles formed by the diagonals share a side (the diagonal), and the angle we have already established is congruent.
The options given relate to various triangle pairs. Considering the relationships established so far, the logical next step would be to focus on the triangles involving the point of intersection (O) and the diagonals (AC and BD).
Among the options presented:
- △DAB ≅ △AOB: This would not work because there is no established equality involving \(OB\).
- △DAB ≅ △DAO: This does not fit with our earlier statements, as \(A\) and \(D\) would not form a valid triangle with \(O\) in terms of proving diagonal congruence.
- △DAB ≅ △CBA: This does not incorporate segment \(AC\) or any criteria that have been established.
- △DAB ≅ △DOC: This triangle pairs include the congruence established in sides and angles and aligns with the idea that diagonals in a rectangle bisect each other, making it a good candidate for showing congruence.
Upon reviewing the options, we conclude that the correct answer is:
△DAB ≅ △DOC.
This is because it employs known congruent angles and sides to establish that both triangles formed around point \(O\) are congruent, driving toward the conclusion that the diagonals \(AC\) and \(BD\) are congruent (since bisecting lines in a rectangle make these triangles congruent through SAS).