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Math Forum » Discussions » Math Topics » geometry.pre-college.independent

Topic: Question about trapezoids
Replies: 7   Last Post: Jul 8, 2008 5:13 AM

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Ara M Jamboulian

Posts: 63
Registered: 12/6/04
Re: Question about trapezoids
Posted: Jan 18, 2007 5:31 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> (Deep breath)
> I've got an isosceles triangle ABC. There's a line
> DE cutting across it which looks like it's parallel
> to the base BC, but we don't know for sure.
>
> The question is, given that the diagonals BE and DC
> are of equal length, show that the quadrilateral BCDE
> is cyclic.
>
> If I could prove that BCDE is an isosceles trapezoid,
> I'd be in business...but I haven't been able to do
> that to my own satisfaction. Is it true that a
> quadrilateral has two equal base angles and diagonals
> of equal length, it must be an isosceles trapezoid?
> If so, could someone please sketch out how you'd
> d prove it? I'm sure I'm missing something obvious.
>
> Thanks,
> JF
BCED is not necessarily isosceles.
So you need to prove cyclic using some other method.

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