Look at the quadrilateral shown below.

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

Question

Look at the quadrilateral shown below.

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

anonymous · Answer

Terra’s proof

1. AO = OC because it is given that diagonals bisect each other. 
2. BO = OD because it is given that diagonals bisect each other. 
3. For triangles AOB and DOC, angle 1 is equal to angle 2 as they are supplemental angles.  
4. Therefore, the triangles AOB and DOC are congruent by SAS postulate. 
5. Similarly, triangles AOD and BOC are congruent. 
6. By CPCTC, angle ABD is equal to angle BDC and angle ADB is equal to angle DBC. 
7. As the alternate interior angles are congruent the opposite sides of quadrilateral ABCD are parallel. 
8. Therefore, ABCD is a parallelogram.

Which is the first incorrect statement in Terra’s proof?

 Statement 2

 Statement 3

 Statement 1

 Statement 4