How do I prove that TUVWXY is a regular hexagon?

[Jonn321]

Given that line UV and XY are parallel, and Z is the midpoint of line UX, prove that TUVWXY is a regular hexagon.

 

[pka]

Given that line UV and XY are parallel, and Z is the midpoint of line UX, prove that TUVWXY is a regular hexagon.

View attachment 18514

As written the statement is false. For example we could have \(U-T-Y\) that is \(U,~T,~\&~Y\) could be colinear.

 

[Steven G]

Might it be given that Z is a midpoint of VY???

 

[pka]

Might it be given that Z is a midpoint of VY???

That does not change the question at all.
Even if that was added does not address the position of \(T~\&~W\).