Here is the organized two-column proof with the correct statements and reasons filled in:
| Statement | Reason | |-----------------------------------------------------|---------------------------------------------------------| | 1. ABCD is a parallelogram. | Given | | 2. DB is congruent with AC. | Given | | 3. DA is congruent with CB. | Opposite sides of a parallelogram are congruent. | | 4. AB is congruent with BA. | Reflexive Property of Congruence | | 5. ∆BAD is congruent with ∆ABC. | SSS Congruence Theorem | | 6. ∆BAD ≅ ∆ABC | CPCTC Theorem of Congruence | | 7. m∠BAD = m∠ABC | Definition of congruence | | 8. m∠BAD + m∠ABC = 180° | Consecutive angles of a parallelogram are supplementary | | 9. m∠BAD + m∠BAD = 180° | Substitution Property of Equality | | 10. 2m∠BAD = 180° | Combine like terms | | 11. m∠BAD = 90° | Division Property of Equality | | 12. m∠ABC = 90° | Transitive Property of Equality | | 13. m∠ADC = m∠DAB = 90° | Opposite angles of a parallelogram are congruent | | 14. m∠BAD, m∠DCB, m∠ABC, and m∠ADC are right angles | Definition of a right angle | | 15. ABCD is a rectangle | Definition of a rectangle |
This format clearly places all statements and reasons in the proper order while making the proof seamless and logical.
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