Question

in a proof that the diagonals of rectangle abcd are congruent, which statement comes just after the statements that \\( \overline { a d } \cong \overline { b c } \\), \\( \overline { a b } \cong \overline { a b } \\), and \\( \angle d a b \cong \angle c b a \\)? (1 point) \\( \triangle d a b \cong \triangle d a o \\) \\( \triangle d a b \cong \triangle c b a \\) \\( \triangle d a b \cong \triangle a o b \\) \\( \triangle d a b \cong \triangle d o c \\)

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 \(\angle DAB\cong\angle CBA\) (right angles in a rectangle).

Step2: Identify the congruent triangles

The triangles \(\triangle DAB\) and \(\triangle CBA\) have two sides (\(\overline{AD}\) and \(\overline{AB}\) for \(\triangle DAB\); \(\overline{BC}\) and \(\overline{AB}\) for \(\triangle CBA\)) and the included angle (\(\angle DAB\) and \(\angle CBA\)) congruent.

Answer:

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