如图,已知A,B,C为不在同一直线上的三点,AA1∥BB1∥CC1,且AA1=BB1=CC
如图,已知A,B,C为不在同一直线上的三点,AA1∥BB1∥CC1,且AA1=BB1=CC
如图,已知A,B,C为不在同一直线上的三点,AA1∥BB1∥CC1,且AA1=BB1=CC1,
1.若AA1⊥平面ABC,且AC=AA1=4,BC=3,AB=5,求证:A1C⊥平面AB1C1
如图,已知A,B,C为不在同一直线上的三点,AA1∥BB1∥CC1,且AA1=BB1=CC1,
1.若AA1⊥平面ABC,且AC=AA1=4,BC=3,AB=5,求证:A1C⊥平面AB1C1
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∵AA1⊥面ABC,BC在面ABC上
∴AA1⊥BC,
又∵BC=3,AC=4,AB=5,
∴BC⊥AC,
∵AA1和AC同在面AA1C1C上,
∴BC⊥面AA1C1C
∵A1C在面AA1C1C上,
∴BC⊥A1C,
∵BB1∥CC1且BB1=CC1,
∴BB1C1C是平行四边形,
∴BC∥B1C1,
∵BC⊥A1C,
∴B1C1⊥A1C,
又∵AC=AA1=A1C1=C1C,AA1⊥AC,
∴AA1C1C是正方形
∵AC1和A1C是两条对角线,
∴AC1⊥A1C,
∵AC1、B1C1同在面AB1C1上,A1C⊥AC1,A1C⊥B1C1,
∴A1C⊥面AB1C1,得证.
∴AA1⊥BC,
又∵BC=3,AC=4,AB=5,
∴BC⊥AC,
∵AA1和AC同在面AA1C1C上,
∴BC⊥面AA1C1C
∵A1C在面AA1C1C上,
∴BC⊥A1C,
∵BB1∥CC1且BB1=CC1,
∴BB1C1C是平行四边形,
∴BC∥B1C1,
∵BC⊥A1C,
∴B1C1⊥A1C,
又∵AC=AA1=A1C1=C1C,AA1⊥AC,
∴AA1C1C是正方形
∵AC1和A1C是两条对角线,
∴AC1⊥A1C,
∵AC1、B1C1同在面AB1C1上,A1C⊥AC1,A1C⊥B1C1,
∴A1C⊥面AB1C1,得证.
1年前
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