Question

Use the image to answer the 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≅△DAO
triangle upper A upper C upper D congruent to triangle upper C upper A upper B

△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≅△CBA

Answer 1

In the proof that the diagonals of rectangle ABCD are congruent, the statement that comes just after the statements \(AD \cong BC\), \(AB \cong AB\), and \(\angle DAB \cong \angle CBA\) is:

\[
\triangle DAB \cong \triangle AOB
\]

This statement follows because you are establishing that triangles \(DAB\) and \(AOB\) are congruent by the Side-Angle-Side (SAS) congruence criterion, which can be derived from the previously mentioned congruent sides and the included angle.