Elba writes the following proof for the theorem, “If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.”

Elba’s proof

1. For triangles AOB and DOC, angle 1 is equal to angle 2 as they are vertical angles.
2. AO = OC and BO = OD because it is given that diagonals bisect each other.
3. Therefore, the triangles AOB and DOC are congruent by SAS postulate.
4. Similarly, triangles AOD and BOC are congruent.
5. By CPCTC, angle ABD is equal to angle CDB and angle ADB is equal to angle CBD.
6. As the corresponding angles are congruent, the opposit

Question

Elba writes the following proof for the theorem, “If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.”

Elba’s proof

1. For triangles AOB and DOC, angle 1 is equal to angle 2 as they are vertical angles.  
2. AO = OC and BO = OD because it is given that diagonals bisect each other. 
3. Therefore, the triangles AOB and DOC are congruent by SAS postulate. 
4. Similarly, triangles AOD and BOC are congruent. 
5. By CPCTC, angle ABD is equal to angle CDB and angle ADB is equal to angle CBD. 
6. As the corresponding angles are congruent, the opposit