Question

the following two - column proof with missing statement proves that the diagonals of the rectangle bisect each other.
statement\treason
abcd is a rectangle\tgiven
ab and cd are parallel\tdefinition of a parallelogram
ad and bc are parallel\tdefinition of a parallelogram
∠cad≅∠acb\talternate interior angles theorem
bc = ad\tdefinition of a parallelogram
∠ade≅∠cbe\talternate interior angles theorem
△ade≅△cbe\tangle - side - angle (asa) postulate
be = de\tcpctc
ae = ce\tcpctc
ac bisects bd\tdefinition of a bisector
which statement can be used to fill in the blank space?
∠adb≅∠cbd
∠abe≅∠ade
∠acd≅∠ace
∠ace≅∠cbd

Explanation:

Step1: Recall ASA postulate requirements

To use the Angle - Side - Angle (ASA) Postulate to prove $\triangle ADE\cong\triangle CBE$, we need two pairs of congruent angles and the included side congruent. We already have $\angle CAD\cong\angle ACB$ and $BC = AD$. We need another pair of angles.

Step2: Identify correct angle pair

Since $AB\parallel CD$ (by definition of parallelogram as rectangle is a parallelogram), $\angle ABE\cong\angle ADE$ are alternate - interior angles. This gives us the second pair of congruent angles for the ASA postulate.

Answer:

$\angle ABE\cong\angle ADE$