Wrong question about parallel sides

[MathsforMaths]

This question appeared in my exam. Look at the figure and join db. Look at the second part of question. It is wrong.

 

[conway]

Im just a philosopher, and a terrible mathematician. So we will have to wait for the pros....but it appears correct to me. (ab) is parallel to (cd). Perhaps I am missing something. Feel free to expand your point. "Proving" that they are is something else....I love when we find mistakes in our mathematics...tickles me to no end. I hope that you are right!

 

[Phrzby Phil]

I agree. Tilt angles BAC and DCA inward identically. Initial conditions still hold.

 

[conway]

Phrzby

Can you expand on this? It would be appreciated!

 

[Phrzby Phil]

Nothing to expand on. Draw the diagram as I said, keeping the initial conditions the same. Since the two sides are now tilted toward each other, they are not parallel.

 

[Phrzby Phil]

By saying "Tilt angles BAC and DCA inward identically," I thought it would be obvious that one could do so by drawing it that way.

But one need not actually draw it - the diagram with identically tilted sides exists whether drawn or not - visualized for example.

It was a "mistake" because it cannot be proved because counter-examples exist - per my suggestion.