如图,△ABC中,AB=AC,AD和BE是高,它们交于H,且AE=BE.求证:AH=2BD.
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![如图,△ABC中,AB=AC,AD和BE是高,它们交于H,且AE=BE.求证:AH=2BD.](/uploads/image/z/1600025-41-5.jpg?t=%E5%A6%82%E5%9B%BE%2C%E2%96%B3ABC%E4%B8%AD%2CAB%EF%BC%9DAC%2CAD%E5%92%8CBE%E6%98%AF%E9%AB%98%2C%E5%AE%83%E4%BB%AC%E4%BA%A4%E4%BA%8EH%2C%E4%B8%94AE%EF%BC%9DBE.%E6%B1%82%E8%AF%81%EF%BC%9AAH%EF%BC%9D2BD.)
如图,△ABC中,AB=AC,AD和BE是高,它们交于H,且AE=BE.求证:AH=2BD.
如图,△ABC中,AB=AC,AD和BE是高,它们交于H,且AE=BE.求证:AH=2BD.
如图,△ABC中,AB=AC,AD和BE是高,它们交于H,且AE=BE.求证:AH=2BD.
AD是等腰△ABC底边上的高,可得:BD = CD ,即有:BC = 2BD .
在△AEH和△BEC中,
∠AEH = 90°= ∠BEC ,AE = BE ,∠EAH = 90°-∠C = ∠EBC ,
所以,△AEH ≌ △BEC ,
可得:AH = BC = 2BD .
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