Here we have that the biggest angle AOD can be written as sums of different angles:
[tex]\begin{gathered} m\angle AOD=m\angle AOC+m\angle COD \\ m\angle AOD=m\angle BOD+m\angle AOB \end{gathered}[/tex]
The transitive property of the equality says that if:
[tex]\begin{gathered} a=c\text{ and }b=c \\ \text{Then} \\ a=b \end{gathered}[/tex]
In our case we have:
[tex]\begin{gathered} a=m\angle AOC+m\angle COD \\ b=m\angle BOD+m\angle AOB \\ c=m\angle AOD \end{gathered}[/tex]
So according to the property:
[tex]m\angle BOD+m\angle AOB=m\angle AOC+m\angle COD[/tex]
And if:
[tex]m\angle AOB=m\angle COD[/tex]
Then we have that:
[tex]\begin{gathered} m\angle BOD+m\angle AOB=m\angle AOC+m\angle COD \\ m\angle BOD+m\angle AOB=m\angle AOC+m\angle AOB \\ m\angle BOD+m\angle AOB-m\angle AOB=m\angle AOC \\ m\angle BOD=m\angle AOC \end{gathered}[/tex]
This means that you can prove the statement "if mAOB=mCOD then mBOD=mAOC" by using the transitive property of the equality. Therefore, the correct option is D.
