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# 直角三角形全等的判定 - PowerPoint PPT Presentation

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### 直角三角形全等的判定

Question:如何判定两个直角三角形全等?

∠B=∠B′=90°

A

A′

B′

C′

B

C

A

B

C

D

B

10cm

10cm

10cm

10cm

10cm

8cm

8cm

8cm

8cm

8cm

A

C

How to do it?

N

M

C

Step1:画∠MCN=90°;

N

M

C

Step1:画∠MCN=90°;

Step2:在射线CM上截取CA=8cm;

A

Step1:画∠MCN=90°;

Step2:在射线CM上截取CA=8cm;

Step3:以A为圆心，10cm为半径画弧，交射线CN于B;

N

B

M

A

C

Step1:画∠MCN=90°;

Step2:在射线CM上截取CA=8cm;

Step3:以A为圆心，10cm为半径画弧，交射线CN于B;

Step4:连结AB;

N

△ABC即为所要画的三角形

B

M

A

C

B ′

B

10cm

10cm

10cm

10cm

10cm

10cm

10cm

10cm

10cm

10cm

Rt△ABC≌

8cm

8cm

8cm

8cm

8cm

8cm

8cm

8cm

8cm

8cm

A′

A

C ′

C

∵∠C=∠C′=90°

∴在Rt△ABC和Rt△ 中

B

B′

AB=

BC=

A

A ′

C

C ′

∴Rt△ABC≌

1.一个锐角及这个锐角的对边对应相等的两个直角三角形.

(AAS)

2.一个锐角及这个锐角相邻的直角边对应相等的两个直角三角形.

(ASA)

3.两直角边对应相等的两个直角三角形.

(SAS)

4.有两边对应相等的两个直角三角形.

(SAS)

(HL)

∴∠C=∠D=90°(垂直的定义)

C

D

A

B

AB=AC

(全等三角形的对应边相等,对应角相等)

A

D

C

B

A

∠BAC=∠EDF, AB=DE,∠B=∠E

B

P

C

D

Rt△ABP≌Rt△DEQ

AB=DE,AP=DQ

E

F

Q

A

B

P

C

D

E

F

Q

∴∠APB=∠DQE=90°

AB=DE

AP=DQ

∴Rt△ABP≌Rt△DEQ (HL)

∴ ∠B=∠E (全等三角形的对应角相等)

∠BAC=∠EDF

AB=DE

∠B=∠E (已证)

∴△ABC≌△DEF (ASA)

“ AAS ”

“ SSS ”

“SAS”

“ ASA ”

“ SAS ”

“ ASA ”

“ AAS ”

“ HL ”

1.书本P55 /2,4,5

2.《课课练》P41-43