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• 一、线段的比

• 线段的比是指用同一长度单位度量的两条线段的长度的比.

• 线段的比与所采用的长度单位无关；

• 两条线段的比是一个没有单位的正数；

• 比例尺是指图上距离与实际距离的比.

(1)比例的基本性质

(等积式与比例式的互化).

ａ∶ｂ=ｃ∶ｄ ａｄ=ｂｃ.

a∶b = b∶c b2 = ac.

A

D

A

L1

L1

E

E

B

L2

B

L2

F

C

F

L3

C

L3

A

D

A

L1

L1

E

E

B

L2

B

L2

F

C

F

L3

C

L3

A

E

L1

L1

D

A

E

L2

L2

B

C

L3

L3

B

C

（二）

（一）

D

E

B

C

∠A= ∠A

∵ DE//BC

F

∴DE=BF,DE=FC

∠A= ∠A

A

∵ DE//BC

D

E

∵DBFE是平行四边形

∴DE=BF

B

C

F

A

E

O

D

E

（图1）

C

B

B

（图2）

C

“X”型

“A”型

3

AB∥EF

△AOB∽ △FOE

AB∥CD

△AOB ∽△DOC

EF∥CD

△EOF∽△COD

G

D

E

O

B

C

F

△AＤＥ

△ＧＦＣ

△ＧＯＥ

E

A

B

D

• 如图,已知DE ∥ BC,AE=50cm,EC=30cm,BC=70cm,

∠BAC=450,∠ACB=400.

DE ∥ BC

∠AED=∠C=400.

（2）

G

D

E

H

I

F

C

B

（1）请找出图中所有的相似三角形；