Question

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 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
∠CAD ≅ ∠ACB Alternate interior angles theorem
Line segment BC is congruent to line segment AD Definition of a Parallelogram
Alternate interior angles theorem
ƒ Δ ADE ≅ ƒ Δ CBE 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?
∠ADB ≅ ∠CBD
∠ABE ≅ ∠ADE
∠ACD ≅ ∠ACE
∠ACE ≅ ∠CBD

Answer 1

∠ADB ≅ ∠CBD

Explanation:

its right bc i tried it

Answer 2

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