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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≅△DAO
triangle upper A upper C upper D congruent to triangle upper C upper A upper B

△DAB≅△CBA
triangle upper A upper O upper B congruent to triangle upper D upper O upper C

△DAB≅△DOC
triangle upper A upper O upper D congruent to triangle upper C upper O upper B
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Answer 1

To prove that the diagonals of rectangle ABCD are congruent, we utilize the properties of triangles and the congruence of their parts. Given the previous statements:

1. \(AD \cong BC\)
2. \(AB \cong AB\) (reflexive property)
3. \(\angle DAB \cong \angle CBA\) (corresponding angles in a rectangle)

The next logical step is to compare triangles that incorporate the intersection point \(O\) of the diagonals \(AC\) and \(BD\).

The best option that logically follows the previous statements is:

△DAB ≅ △CBA
This states that triangle ADB is congruent to triangle CBA, using Side-Angle-Side (SAS) congruence because we have already established two pairs of corresponding sides and the included angle.

Thus, the correct response is:

△DAB≅△CBA (triangle ADB congruent to triangle CBA).