Question

a student claims that a 180 degree rotation of a vertical angle will always map to the other vertical angle thus proving that they are congruent. the teacher asks how the student knows that 180 degrees will land it exactly on the vertical angle. how should the student respond ?

Answer 1

Given: A 180 degree rotation of a vertical angle will always map to the other vertical angle

To Determine: The prove that the vertical angles are congruent

Draw and label to vertical lines with an angle

The 180 degree rotation of the vertical angle BOC would give:

Note that the other vertical would be AOD

The students should respond that

`\begin{gathered} m\angle BOC\cong m\angle\text{AOD} \\ \text{This is because vertically opposite angles are equal} \end{gathered}`

Hence, the 180 degree rotation of a vertical angle will always map to the other vertical angle which are congruent to each other because:

The vertical angles are vertically opposite to each other