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Answer:
The query asks whether a quadrilateral is a parallelogram. The quadrilateral ABCD is indeed a parallelogram. Here's a step-by-step explanation:
1. **Opposite sides are congruent**:
- AB ≅ CD
- AD ≅ BC
2. **Consecutive angles are supplementary**:
- ∠DAB and ∠ABC are supplementary.
- ∠ABC and ∠BCD are supplementary.
- ∠BCD and ∠CDA are supplementary.
- ∠CDA and ∠DAB are supplementary.
3. **Opposite angles are congruent**:
- ∠DAB ≅ ∠DCB
- ∠CBA ≅ ∠CDA
4. **Diagonals bisect each other**:
- O is the midpoint of BD.
- O is the midpoint of AC.
5. **Each diagonal divides the quadrilateral into two congruent triangles**:
- ΔABD ≅ ΔCBD
- ΔABC ≅ ΔADC