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June 26th, 2011, 08:43 PM   #1
 
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intersection of diagonals of a trapezoid

I have an isosceles trapezoid, of which I know the following information: the lenght of sides, long base and diagonals. How can I find the shorter base and the height? I have been trying to find similar triangles, but everytime I do it seems that they both have too many unknowns to help. What am I missing? Is there something that can help me about where the diagonals intersect? Thanks for any help!!
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June 26th, 2011, 10:38 PM   #2
 
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a, b, c, d and h are shorter base, diagonals, sides, long base and height respectively.

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June 27th, 2011, 12:57 PM   #3
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Re: intersection of diagonals of a trapezoid

Since an isoceles trapezoid is a cyclic quadrilateral, Ptolemy's theorem may be of interest:

http://en.wikipedia.org/wiki/Cyclic_...eral#Diagonals
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