Question

等腰梯形ABCD中,AD‖BC,AB=DC,∠B=60度,对角线AC平分∠BCD,AE‖DC,说明四边形AECD的形状

Answer 1

AD//BC,AE//DC=>四边形AECD的形状是平行四边形

AE//DC=>∠AEB=∠DCB=∠ABC=60°=>AE=AB=BE

对角线AC平分∠BCD=>∠ACB=30°=>∠BAC=90°

=>∠CAE=30°

∴AE=CE

∴平行四边形AECD是菱形