Question

The following two-column proof with missing statement proves that the diagonals of the rectangle bisect each other:
Statement Reason
ABCD is a rectangle. Given
Line segment AB and Line segment CD are parallel | Definition of a Parallelogram
Line segment AD and Line segment BC are parallel | Definition of a Parallelogram
______________ |Alternate interior angles theorem
Line segment BC is congruent to line segment AD | Definition of a Parallelogram
∠ADB ≅ ∠CBD | Alternate interior angles theorem
ΔADE ≅ ΔCBE | Angle-Side-Angle (ASA) Postulate
Line segment BE is congruent to line segment DE CPCTC
Line segment AE is congruent to line segment CE CPCTC
Line segment AC bisects Line segment BD Definition of a bisector
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Which statement can be used to fill in the blank space?
∠ABD ≅ ∠DBC
∠CAD ≅ ∠ACB
∠BDA ≅ ∠BDC
∠CAB ≅ ∠ACB

Answer 1

ab ≅ cd

Explanation:

ab is parallel to cd because they are next to each other but will never cross

Answer 2

∠CAD ≅ ∠ACB

Explanation:

The justification states "alternate interior angles theorem." Alternate interior angles would be inside the parallel lines and on opposite sides of the transversal. The only pair of angles in our choices that fits this definition is ∠CAD and ∠ACB .