Look at the quadrilateral shown below

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

Melissa’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. The triangles AOB and DOC are congruent by SSS postulate.
4. Similarly, triangles AOD and BOC are congruent.
5. By CPCTC, AB is equal to DC.
6. By CPCTC, AD is equal to BC.
7. As the opposite sides are congru

Question

Look at the quadrilateral shown below


Melissa writes the following proof for the theorem, “If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.”

Melissa’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. The triangles AOB and DOC are congruent by SSS postulate. 
4. Similarly, triangles AOD and BOC are congruent. 
5. By CPCTC, AB is equal to DC. 
6. By CPCTC, AD is equal to BC. 
7. As the opposite sides are congru

anonymous · Answer

Statement 5 

 Statement 3 

 Statement 4 

 Statement 6