Help with Proofs on quadrilaterals please?

Question

anonymous · Answer

The figure below shows rectangle ABCD.
 Rectangle ABCD with diagonals AC and BD passing through point E
 
The 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

Triangle ADE is congruent to triangle 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 ACbisects 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

anonymous · Answer

The blank needed filled is for Alternate interior angles theorem I also have a picture

anonymous · Answer

oops wrong photo sorry about that...

anonymous · Answer

attachment

anonymous · Answer

it could be
∡BCA is congruent to ∡CAD

anonymous · Answer

I think its CAD ≅ ∡ACB

anonymous · Answer

well..

Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternate interior angles are congruent.

anonymous · Answer

what do you think is right?

anonymous · Answer

We have the same idea, if you didn't notice :D