Question

已知直角梯形ABCD中,AD平行BC,AB垂直BC,AD加BC等于AB,点O是CD中点,连接OA,OB尝试判断三角形AO

Answer 1

延长AO交BC延长线于E,

∵AD∥BC,∴∠OAD=∠E,∠D=∠OCE,

∵OC=OD,∴ΔOAD≌ΔOEC,

∴OA=OE,AD=CE,

∵AB=AD+BC=BC+CE=BE,

∴AB=BE,又OA=OE,

∴BO⊥AE,

∴ΔAOB是直角三角形.