Solution:
Given:
[tex]\begin{gathered} 1)Po\text{ int Z is the midpoint of WX and VY} \\ 2)WZ=XZ \\ 3)VZ=YZ \end{gathered}[/tex]
To complete the proof,
[tex]\begin{gathered} 4)m\angle VZW=m\angle YZX\ldots\ldots\ldots\ldots.\ldots(vertical\text{ angles theorem)} \\ \text{The two angles are vertically opposite to each other} \end{gathered}[/tex]
The figure can now be split into two triangles as shown below;
From the image drawn above showing corresponding parts of both triangles, we can deduce that,
[tex]\begin{gathered} 5)\Delta VZW\cong\Delta YZX\ldots\ldots\ldots..(side-angle-side\text{ congruency theorem)} \\ \\ \text{The two triangles are congruent by SAS having 2 corresponding equal sides and 1 corresponding equal angle.} \end{gathered}[/tex]
Since the two triangles have been proven to be congruent, then
[tex]6)\angle Y=\angle V\ldots\ldots\ldots\ldots\ldots.(Correspond\text{ ing parts of congruent triangles are congruent)}[/tex]
Therefore,
[tex]7)m\angle Y=m\angle V=48^0\ldots.\ldots\ldots\ldots\ldots\ldots\ldots\text{.(congruent angles have equal measure)}[/tex]
Thus, the correct table that correctly completes the students proof is;
