The figure below shows rectangle ABCD:The following two-column proof with missing statement proves that the diagonals of the rectangle bisect each other: Statement ReasonABCD is a rectangle. GivenLine segment AB and Line segment CD are parallel Definition of a ParallelogramLine segment AD and Line segment BC are parallel Definition of a Parallelogram∠CAD ≅ ∠ACB Alternate interior angles theoremLine segment BC is congruent to line segment AD Definition of a ParallelogramAlternate interior angles theoremƒ Δ ADE ≅ ƒ Δ CBE Angle-Side-Angle (ASA) PostulateLine segment BE is congruent to line segment DE CPCTCLine segment AE is congruent to line segment CE CPCTCLine segment AC bisects Line segment BD Definition of a bisectorWhich statement can be used to fill in the blank space? ∠ADB ≅ ∠CBD ∠ABE ≅ ∠ADE ∠ACD ≅ ∠ACE ∠ACE ≅ ∠CBD
Accepted Solution
A:
Answer:Given : A rectangle A B CDTo Prove: Diagonals of the rectangle bisect each otherProof: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 ParallelogramIn Δ A DE and Δ C BEAD=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) PostulateBE=DE→→[C P CT ]A E=CE→→[C P CT ]⇒Line segment AC bisects Line segment B D⇒Definition of a bisectorBlank Space : Option A⇒∠ADB ≅ ∠CBD