B C A 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 AB and CD are parallel Definition of a Parallelogram AD and BC are parallel Definition ofa Parallelogram 2CADLACB Alternate interior angles theorem Definition of a Parallelogram Alternate interior angles theorem Angle-Side-Angle (ASA) Postulate CPCTC ADB 2CBD AADE ACBE BE DE AE CE CPCTC AC bisects BD Definition of a bisector Which statement can be used to fill in the blank space? (S points) Oa AB CD Ob BE AE BE CE Od BCAD

Given : A  rectangle A B CD

To Prove: Diagonals of the rectangle bisect each other

Proof:

1. ABCD is a rectangle.  

→AB ║CD→ Definition of a Parallelogram

→AD║BC→ Definition of a Parallelogram

⇒∠CAD ≅ ∠ACB  →→[Alternate interior angles theorem]

⇒Line segment BC ≅ Line segment DA→→Definition of a Parallelogram

In  Δ A DE and Δ C BE

AD=BC⇒Proved above

∠CAD=∠ACB ⇒Alternate interior angles theorem

∠ADB=∠CBE ⇒Alternate interior angles theorem

→→Δ A DE ≅  Δ C BE⇒Angle-Side-Angle (A S A) Postulate

BE=DE→→[C P CT ]

A E=CE→→[C P CT ]

⇒Line segment AC bisects Line segment B D⇒Definition of a bisector

Blank Space : Option A⇒∠ADB ≅ ∠CBD