Question

use the image to answer the question.

in a proof that the diagonals of rectangle ( abcd ) are congruent, which statement comes just after the statements that ( overline{ad} cong overline{bc} ), ( overline{ab} cong overline{ab} ), and ( angle dab cong angle cba )?

( \triangle dab cong \triangle doc )
( \triangle dab cong \triangle cba )
( \triangle dab cong \triangle aob )
( \triangle dab cong \triangle dao )

Explanation:

Step1: Recall the Side - Angle - Side (SAS) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In rectangle \(ABCD\), we have \(\overline{AD}\cong\overline{BC}\), \(\overline{AB}\cong\overline{AB}\) (common side), and \(\angle DAB\cong\angle CBA\) (angles of a rectangle are right angles, so they are congruent).

Step2: Identify the congruent triangles

The triangles that have the two sides (\(\overline{AD}\), \(\overline{AB}\)) and the included angle (\(\angle DAB\)) for one triangle and the two sides (\(\overline{BC}\), \(\overline{AB}\)) and the included angle (\(\angle CBA\)) for the other triangle are \(\triangle DAB\) and \(\triangle CBA\).

Answer:

\(\triangle DAB\cong\triangle CBA\)