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The figure below shows rectangle ABCD.. The two-column proof with missing statement proves that the diagonals of the rectangle bisect each other. . . . Statement. . Reason. . ABCD is a rectangle.. . Given. . and are parallel. . Definition of a Parallelogram. . and are parallel. . Definition of a Parallelogram. . . . Alternate interior angles theorem. . . . Definition of a Parallelogram. . ∡ADB ≅ ∡CBD. . Alternate interior angles theorem. . . . Angle-Side-Angle (ASA) Postulate. . . . CPCTC. . . . CPCTC. . bisects . . Definition of a bisector. . . . Which statement can be used to fill in the blank space?. . ∡ABD ≅ ∡DBC. . ∡CAD ≅ ∡ACB. . ∡BDA ≅ ∡BDC. . ∡CAB ≅ ∡ACB

Respuesta :

meerkat18
          STATEMENT                            REASON
1) ABCD is a rectangle                   Given
     __         __
2) AB and CD are parallel              Definition of a Parallelogram
     __         __
3) AD and BC are parallel              Definition of a Parallelogram

4) _________________                Alternate Interior Angles Theorem
    __      __
5) BC ≡ AD                                   Definition of a Parallelogram

6) ∡ ADB ≡ ∡ CBD                       Alternate Interior angles theorem

7) VADE ≡ VCBE                          Angle-Side-Angle (ASA) Postulate
     __     __
8)  BE ≡ DE                                  CPCTC
     __    __
9) AE ≡ CE                                    CPCTC
       __             __
10) AC bisects BD                         Definition of a bisector

Which statement can be used to fill in the blank space?
1) ∡ABD ≅ ∡DBC 
2) ∡CAD ≅ ∡ACB       THIS IS THE CORRECT ANSWER FOR #4.
3) ∡BDA ≅ ∡BDC

Answer:

∡CAD ≅ ∡ACB  

Step-by-step explanation:

In the figure attached, a best description of the problem is shown .

The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

In this case, the parallels are segments AD and BC. Then, the theorem tell us that angles ∡CAD and ACB are congruent.

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