Mowaffaq Hajja, A very short and simple proof of ``the most
elemetary theorem'' of euclidean geometry,
Forum Geometricorum, 6 (2006) 167--169.
Abstract: We give a very short and simple proof of the fact that if ABB'
and AC'C are straight lines with BC and B'C' intersecting at D, then
AB + BD = AC' + C'D if and only if AB' + B'D = AC + CD. The ``only if" part
is attributed to Urquhart, and is referred to by Dan Pedoe as ``the most elementary
theorem of Euclidean geometry".
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