DE =半AB? ?
证明如下:在
AD BC高,是高在AC,∠C = 60°的Rt△ADC的Rt△BEC中
CDS = ACcos∠C = CAcos60°= 0.5CA
CE = BCcos∠C = CBcos60°= 0.5CB
在△DCE和△ACB
CD:CE = 0.5CA:0.5CB
对应的角度∠DCE =∠ACB = 60°(实际上是相同的角度)
∴△DCE∽△ACB
∴DE:AB = CD:CA = CA:CB = 0.5CA:CA = 1:2
∴DE =半AB