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

Question

In a proof that the diagonals of rectangle ABCD are congruent, which statement comes just after the statements that line AD≅ line BC, line AB ≅ AB, and angle DAB ≅ angle CBA?
A. triangle DAB ≅ triangle DOC 
B. triangle DAB ≅ triangle CBA 
C. triangle DAB ≅ triangle DAO 
D. triangle DAB ≅ triangle AOB

GPT-4o mini · Answer

In a proof that the diagonals of rectangle ABCD are congruent, the statements you're referring to establish the congruence of the corresponding sides and angles of triangles formed by the diagonals and the sides of the rectangle.

The correct statement that would logically follow after establishing that line AD ≅ line BC, line AB ≅ line AB, and angle DAB ≅ angle CBA would be:

B. triangle DAB ≅ triangle CBA

This is because the sides and angles established lead to the conclusion that these two triangles (DAB and CBA) are congruent, which is a necessary step in proving that the diagonals (AC and BD) of the rectangle are congruent.