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In the following diagram, giving we do not know that XZ is parallel to YV, prove that $WX=XY$. I have marked the values I do know are equal, but I am a bit stuck about continuing.

enter image description here

Jamminermit
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  • if you don't know that XZ is parallel to VY then what you are trying to prove is not always correct. – atul ganju Jul 02 '20 at 17:34
  • Ah yes, that is true. Is there a way to prove that XZ is parallel to VY from the given information? – Jamminermit Jul 02 '20 at 17:35
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    I don't believe there is. Call that middle point where the diagonals meet D. DX will always be equal in length to DZ regardless of whether or not XZ is parallel to VY. You can see this by taking XZ to the extreme and making X become W and Z become V. In this case all the given information still remains true. – atul ganju Jul 02 '20 at 17:38
  • The thesis is in general false, no way then to prove it. – Intelligenti pauca Jul 03 '20 at 08:38

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