如图所示，四棱锥S﹣ABCD的底面ABCD为等腰梯形，AB∥CD，对角线AC与BD交于点O，OA=3，OD=1，CD=2，SO⊥底面ABCD．求证：SA⊥BD

题干

如图所示，四棱锥S﹣ABCD的底面ABCD为等腰梯形，AB∥CD，对角线AC与BD交于点O，OA=3，OD=1，CD=2，SO⊥底面ABCD．

求证：SA⊥BD

上一题下一题 0.0难度选择题更新时间:2020-02-10 07:50:47

证明：∵OD=1，底面ABCD这等腰梯形，

∴OC=1，又CD=2，∴OC⊥OD，

∴AC⊥BD，又SO⊥底面ABCD，∴BD⊥SO，

∵AC∩SO=0，

∴BD⊥平面SOA，

∴SA⊥BD．

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