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:

mellissa’s proof

1. for triangles aob and cod, 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 are congruent by sas postulate

4. similarity, triangles aod and cob and congruent

5. by cpctc, ab is equal to dc

6. by cpctc, ad is equal to bc

7. as the opposite sides are congruent, the quadrilateral abcd is a parallelogram.

which is the missing phrase in melissa’s proof?

a. angles adb and cbd
b. angles aob and cod
c. triangles adb and cbd
d. triangles aob and cod