In a proof that the diagonals of rectangle ABCD are congruent, which statement comes after the statements that AD ≅ BC, AB ≅ AB, and angle DAB ≅ angle CBA?

Question

a. triangle DAB ≅ triangle CBA
b. triangle DAB ≅ triangle DAO
c. triangle DAB ≅ triangle DOC
d. triangle DAB ≅ triangle AOB

Answer 1

In the proof that the diagonals of rectangle ABCD are congruent, after the statements that \( AD \cong BC \), \( AB \cong AB \) (reflexive property), and \( \angle DAB \cong \angle CBA \), the next logical step would typically be:

d. triangle DAB ≅ triangle AOB

This is because you would be using the Side-Angle-Side (SAS) congruence postulate to show that triangles DAB and AOB are congruent, leading towards proving that the diagonals AC and BD are equal.