Question

(1 point) 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?
△dab ≅ △cba
△dab ≅ △doc
△dab ≅ △dao
△dab ≅ △aob

Explanation:

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

The SAS 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 are given \(\overline{AD}\cong\overline{BC}\), \(\overline{AB}\cong\overline{AB}\) (common side), and \(\angle DAB\cong\angle CBA\) (right angles in a rectangle).

Step2: Identify the triangles

We need to check which pair of triangles uses these congruent parts.
\(\triangle DAB\) and \(\triangle CBA\) have:

• \(AD = BC\) (given)
• \(AB=BA\) (common side)
• \(\angle DAB=\angle CBA\) (right angles in a rectangle)

Answer:

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