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# 勾股定 理的用法及启发 - PowerPoint PPT Presentation

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### 勾股定理的用法及启发

a2+b2=c2

B

C

A

B

C

A

∴在Rt△ABC中,

AB2=AC2-BC2=262-242=100

∵AB＞0

∴AB=10(m)

∴在Rt△ABC中,由勾股定理得

AB2=AC2+BC2=62+82=100

∴AB=10(cm)

∴BE= AB- AE=10-6=4(cm)，

∠BED = ∠AED=∠ACB＝90°

DB=8-x(cm)

DB2=DE2+BE2

(8-x)2=x2+42

6

10

6

4

x

x

8-x

8

A

B

C

A

B

C

S1=πR12，S2=πR22，S3=πR32

BC2+AC2=AB2

(2R1)2+ (2R2)2= (2R3)2

∴R12+ R22= R32

∴πR12+πR22=πR32

C

B

B

A

A

9

12

15

BC=6cm,求三角形的面积。

A

B

C

A

B

C

D

(1)、知道直角三角形其中两边的长度直接求第三边的长度。

(2)、把勾股定理的等量关系转化为方程进行求值。

(3)、把勾股定理的结果用于证明题的推理过程。