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# 相似三角形的性质及其应用 - PowerPoint PPT Presentation

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## PowerPoint Slideshow about ' 相似三角形的性质及其应用' - truong

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D

D

A

E

F

B

C

A

B

F

E

C

D

D

A

A

B

F

E

C

E

F

B

C

∵太阳的光线是平行的

∴ AB∥DE

∴∠ABC= ∠DEF

∵人与旗杆是垂直于地面的

∴∠ACB= ∠DFE=900

∴△ABC∽△DEF

C

E

1

3

2

A

M

N

B

F

D

H

C

E

A

2

M

N

3

B

F

D

H

∵人、标杆和旗杆是互相平行的

∵EF∥CN

∴ ∠1= ∠2

∴△AME∽△ANC

1

∵人与标杆的距离AM、人与旗杆的距离AN、标杆与人眼到地面距离的差EM都可测量出

∴能求出CN

∵四边形ABND为矩形

∴DN=AB

∴能求出旗杆CD的高度CD=CN+DN

C

C

A

A

1

2

B

E

D

B

E

D

A

∴∠ABC=∠A\'B\' C\'

∴ ∠ACB =∠ C\'=90º

∴△ABC∽△ A\'B\' C\'

∴AC=6

AE=AC+CE=6+2=8

A\'

C\'

B\'

C

B

E

D

A

A\'

1

?

B

C\'

E

B\'

1.5

2

C

D

9

A

A\'

?

B

C

1

2

C\'

E

9

B\'

D

1.5

∴四边形ACDB为平行四边形

∴旗杆的上半部分AC与墙上的影子BD的长度是相同的

A

C

A\'

B

1

2

C\'

E

B\'

1.5

9

D

A

A\'

B

1

2

C\'

E

1.5

9

B\'

A

A\'

B

1

2

C\'

60

E

1.5

9

B\'

Q

B

A

C

O

P

1 、 测高(不能直接使用皮尺或刻度尺量的)

2 、 测距(不能直接测量的两点间的距离)

③利用相似解决问题

AE

PN

=

AD

BC

80–x

x

=

80

120

1、如图，△ABC是一块锐角三角形余料，边BC=120毫米，高AD=80毫米，要把它加工成正方形零件，使正方形的一边在BC上，其余两个顶点分别在AB、AC上，这个正方形零件的边长是多少？

A

E

N

P

C

B

Q

D

M