Question

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

Answer 1

∡CAD ≅ ∡ACB

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.

Answer 2

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

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

6) ∡ ADB ≡ ∡ CBD Alternate Interior angles theorem

7) VADE ≡ VCBE Angle-Side-Angle (ASA) Postulate
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8) BE ≡ DE CPCTC
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9) AE ≡ CE CPCTC
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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