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Guest Message by DevFuse

# parallelogram conjecture?

Best Answer bonanova, 28 May 2013 - 05:21 AM

What about the other part of the conjecture that the area is half?

Spoiler for Looks like

Spoiler for Area proof

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5 replies to this topic

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Posted 27 May 2013 - 12:25 AM

Start with any general quadrilateral, and connect the midpoints of consecutive sides, making an inscribed quadrilateral as in the diagram. That inscribed quadrilateral, in the diagram, seems to be a parallelogram. Let me conjecture that this inscribed quadrilateral is a parallelogram with half the area of the original quadrilateral. Can you prove or disprove either part of my conjecture?

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Posted 27 May 2013 - 01:58 AM

Which diagram? I'm not seeing one.

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Posted 27 May 2013 - 03:15 AM

Which diagram? I'm not seeing one.

oops.  nice catch.  I forgot to upload it.  but it is meant to just show an arbitrary quadrilateral, see below:

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### #4 bonanova

bonanova

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Posted 27 May 2013 - 03:12 PM

Spoiler for Looks like

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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Posted 27 May 2013 - 05:32 PM

What about the other part of the conjecture that the area is half?

Spoiler for Looks like

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### #6 bonanova

bonanova

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Posted 28 May 2013 - 05:21 AM   Best Answer

What about the other part of the conjecture that the area is half?

Spoiler for Looks like

Spoiler for Area proof

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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