Question

如图,在梯形ABCD中,AB‖DC,M为AB中点,CM为∠BCD的平分线,求证：BC=AB+CD

Answer 1

条件M为AB中点应该为：M为AD得中点

证明：连接CM交BA的延长线于H,∵AB‖DC,∴∠D=∠HAM,∠H=∠DCM,∵M为AD的中点

∴⊿CDM≌⊿HAM,∴CM=HM,AH=CD,∵CM为∠BCD的平分线,∴∠DCM=∠BCM,

∴∠H=∠BCM,∴BC=BH∴CB=AB+CD