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June 26th, 2011, 08:43 PM  #1 
Joined: Jun 2011 Posts: 2 Thanks: 0  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!! 
June 26th, 2011, 10:38 PM  #2 
Joined: Apr 2007 Posts: 2,141 Thanks: 0 
a, b, c, d and h are shorter base, diagonals, sides, long base and height respectively. 
June 27th, 2011, 12:57 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 6,101 Thanks: 314 Math Focus: Elementary mathematics and beyond  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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