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# 二面角 (2) - PowerPoint PPT Presentation

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## PowerPoint Slideshow about '二面角 (2)' - wei

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### 二面角 (2)

α

ι

α

ι

β

β

p

β

p

α

ι

β

ι

β

p

α

P

B

γ

α

A

ι

2、求二面角的平面角方法

1、定义

—定义法

①点P在棱上

—三垂线定理法

②点P在一个半平面上

—垂面法

③点P在二面角内

B

A

B

A

B

O

A

α

M

P

O

A

B

N

β

C

∴CO=a，DO=a，PC a ，PD a

∴CD=PC a

O

P

C

D

∠COD是二面角α-AB-β的平面角

a

∴∠COD=90º

P

B

β

α

A

ι

∵PA⊥α ∴PA⊥ι

∵PB⊥β ∴PB⊥ι

O

∴ι⊥平面PAB

∴∠AOB为二面角α–ι–β的平面角

∴∠P= 60º ∴∠AOB=120º

∴这二面角的度数为120º

P

∴OE∥BC且OE BC

E

B

A

P

O

C

O

E

∴所求的二面角P-AB-C 的正切值为

∵O为 AC 中点， ∠ABC=90º

OE⊥AB ，因此 PE⊥AB

∴∠PEO为二面角P-AB-C 的平面角

B’

D

α

C

β

C

O

O

A

A

B

B

D

A为二面角α– CD –β的棱CD上一点，AB在平面α内且与棱CD成45º角，又AB与平面β成30º，求二面角α– CD – β的大小。

α

B

C

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A

β