∵ABC－A′B′C′是直三棱柱,∴B′C′＝BC,∠ABD＝∠C′B′D＝90°.由勾股定理,有：C′D^2＝B′C′^2＋B′D^2＝BC^2＋B′D^2,　AD^2＝AB^2＋BD^2.而AB＝BC、BD＝B′D,∴C′D^2＝AD^2,∴C′D＝AD,又AE＝C′E,∴DE⊥AC...