Explain how to prove that the statement overline (AC)cong overline (DB) is true. angle BADcong by the Alternate Interior Angles Theorem AD overline (AD)cong by the Reflexive Proper Segment Congruence Therefore Delta ACDcong by the square Congruence Theorem . Because corresponding parts of congruent t triangles are congruent, overline (AC)cong overline (DB) angle CDA angle BDA angle CAD &SAS : AÁS - : ASA Delta BDA Delta DBA

<p> The question asks to prove that AC ≅ DB given certain geometric relationships and theorems.<br /><br />1. The statement begins with an assumption that ∠BAD ≅ ∠___ by the Alternate Interior Angles Theorem. The correct angle to compare with ∠BAD under this theorem would be ∠CDA, as these angles are alternate interior angles if lines AC and DB are cut by a transversal.<br /><br />2. The statement then mentions AD ≅ AD by the Reflexive Property of Segment Congruence, which is a valid statement as any segment is congruent to itself.<br /><br />3. The conclusion states that △ACD ≅ △___ by the Congruence Theorem. To determine the congruent triangle and the correct congruence theorem, we must consider the information given. We have two pairs of congruent angles (∠BAD ≅ ∠CDA and ∠DAC ≅ ∠DAC) and a common side (AD ≅ AD). This matches the criteria for the Angle-Angle-Side (AAS) Congruence Theorem, indicating that △ACD ≅ △BDA.<br /><br />4. Finally, since corresponding parts of congruent triangles are congruent, AC ≅ DB.<br /><br />Therefore, the correct fill-ins for the blanks are: <br />- ∠CDA for the first blank, as it is the angle congruent to ∠BAD by the Alternate Interior Angles Theorem.<br />- △BDA for the second blank, as it is the triangle congruent to △ACD by the AAS Congruence Theorem.</p>