Question

In the figure, m∠AOB = m∠COD. Which property of equality will you use to prove m∠AOC = m∠BOD?Question options:A) SymmetricB) AdditionC) SubtractionD) Transitive

Answer 1

Sorry I got the D wrong. What would be the correct answer.

Explanation:

Answer 2

Here we have that the biggest angle AOD can be written as sums of different angles:

`\begin{gathered} m\angle AOD=m\angle AOC+m\angle COD \\ m\angle AOD=m\angle BOD+m\angle AOB \end{gathered}`

The transitive property of the equality says that if:

`\begin{gathered} a=c\text{ and }b=c \\ \text{Then} \\ a=b \end{gathered}`

In our case we have:

`\begin{gathered} a=m\angle AOC+m\angle COD \\ b=m\angle BOD+m\angle AOB \\ c=m\angle AOD \end{gathered}`

So according to the property:

`m\angle BOD+m\angle AOB=m\angle AOC+m\angle COD`

And if:

`m\angle AOB=m\angle COD`

Then we have that:

`\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}`

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.