text: Sorry. But that's not how it works.\n\nIsosceles, from Gk. isoskeles "with equal sides," from isos "equal" + skelos "leg".\n\nIf the legs aren't congruent, it's not isoceles.\n\nThere is nothing to prove.\n\nOn the otherhand if the statement of your problem is  that the base angles of the trapazoid are equal, then you prove it like this.\n\n\nLabel the corners of of your trapazoid A,B,C,D such that AB, BC, CD, and AD are sides, \nAB and CD are the parallel sides, and AB is shorter than CD.\n\nADC and BCD will be equal angles, so will BAD and ABC.\n\nExtend the lines AD and BC until they meet. Label the point E.\n\nSince ADC and BCD are equal, the triangle CDE is isoceles as is the triangle ABE.\n\nSo you have DE = CE and AE = BE, so AD = DE-AE = CE-BE = BC.