The figure below shows rectangle abcd.
the two-column proof with missing statement proves that the diagonals of the rectangle bisect each other.

statement

reason

abcd is a rectangle.

given

and are parallel

definition of a parallelogram

and are parallel

definition of a parallelogram

alternate interior angles theorem

definition of a parallelogram

∡adb ≅ ∡cbd

alternate interior angles theorem

angle-side-angle (asa) postulate

cpctc

cpctc

bisects

definition of a bisector

which statement can be used to fill in the blank space?

∡abd ≅ ∡dbc

∡cad ≅ ∡acb

∡bda ≅ ∡bdc

∡cab ≅ ∡acb

To Prove the diagonals of the rectangle bisect each other, Statement with reason is given:

Statement  ABCD is a rectangle.

Reason:Given

Statement

:Opposite sides are parallel.(AB║DC)

Reason: Definition of a Parallelogram

Statement

:Opposite sides are parallel.(AD║BC)

Reason: Definition of a Parallelogram

Statement

:∠CAB ≅ ∠ ACB

Reason: Alternate interior angles theorem

Statement

: ∠ADB ≅ ∠CBD

Reason:  Alternate interior angles theorem

Option D:∠CAB ≅ ∠ ACB

In ΔAED and ΔBEC

∠CAB ≅ ∠ ACB→→Alternate interior angle,as AB║DC.

∠ADB ≅ ∠CBD→→Alternate interior angle,as AD║BC.

AD=BC→→Opposite sides in a rectangle are equal.

ΔAED ≅ ΔBEC⇒⇒[ASA]

AE=EC→[CPCTC]

BE=ED→[CPCTC]

x/3-10=8

x/3=18

x=48