The figure below shows rectangle ABCD:
Rectangle ABCD with diagonals AC and BD passing through point E
The following two-column proof with a 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