Question

Consider the figure, where point Z is the midpoint of segments WX and VY, and the measure of angle Y is 48 degree A students begins to prove m

Answer 1

Given:

`\begin{gathered} 1)Po\text{ int Z is the midpoint of WX and VY} \\ 2)WZ=XZ \\ 3)VZ=YZ \end{gathered}`

To complete the proof,

`\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}`

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,

Since the two triangles have been proven to be congruent, then

`6)\angle Y=\angle V\ldots\ldots\ldots\ldots\ldots.(Correspond\text{ ing parts of congruent triangles are congruent)}`

Therefore,

`7)m\angle Y=m\angle V=48^0\ldots.\ldots\ldots\ldots\ldots\ldots\ldots\text{.(congruent angles have equal measure)}`

Thus, the correct table that correctly completes the students proof is;