in a proof that the diagonals of rectangle ABCD are congruent, which statement comes just after the statements that AD is congruent BC, AB, is congruent with AB, and DAB is congruent with CBA

DAB is congruent with AOB
DAB is congruent with CBA
DAB is congruent with DAO
DAB is congruent with DOC

1 answer

In a proof that the diagonals of rectangle ABCD are congruent, after establishing that \( AD \cong BC \), \( AB \cong CD \), and \( \angle DAB \cong \angle CBA \), the next statement to include would be related to the triangles formed by the diagonals.

The correct option following those congruences is often to highlight the two triangles formed by the diagonals \( AC \) and \( BD \). A commonly used statement in this context is:

DAB is congruent with DOC.

This foundational result helps establish that the triangles formed by these angles and the sides of the rectangle are congruent, leading to the conclusion that the diagonals are of equal length. However, it's essential to clarify the specific triangles referred to can vary based on the notation and the setup of the proof. If the options were different, just ensure you check the corresponding angles and sides carefully.

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