Geodesic
Characterizations of inner product spaces through an isosceles trapezoid property
Archivum mathematicum, Tome 35 (1999) no. 1, pp. 21-27.

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Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.
Classification : 46C15
Keywords: inner product space; norm derivative $\rho ^{\prime }_{\pm }$; heights 
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     title = {Characterizations of inner product spaces through an isosceles trapezoid property},
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Alsina, C.; Cruells, P.; Tomás, M. S. Characterizations of inner product spaces through an isosceles trapezoid property. Archivum mathematicum, Tome 35 (1999) no. 1, pp. 21-27. http://geodesic.mathdoc.fr/item/ARM_1999__35_1_a2/