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

△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
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Answer 1

To prove that the diagonals of rectangle ABCD are congruent, you would typically show that the two triangles formed by the diagonals (e.g., triangles AOB and COD) are congruent. The given statements include the information needed to invoke the criteria for triangle congruence.

The correct statement that follows the ones about AD ≅ BC, AB ≅ AB, and ∠DAB ≅ ∠CBA is:

△DAB ≅ △CBA

Therefore, the response would be: △DAB≅△CBA (triangle AOB is congruent to triangle DCO). This indicates that the necessary congruences exist to show that the diagonals are equal in length.