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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. a 2 + b 2 = c 2. 主讲: 佛山市三水区西南街道第二中学 李建豪. 勾股定理是中学阶段非常重要的定理。在几何计算和证明中有着广泛的应用。俗话说得好,“ 学以致用 ”。学完 勾股定 理之后,就要应用。经总结和归纳, 勾股定 理一共有三大用法,下面我们逐一加以介绍,并从中得到一些学习上的 有益启发 。. B. C. A. 用法一. 知道直 角三角形其中两边的长度直接求第三边的长 度。

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勾股定 理的用法及启发

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5585910

a2+b2=c2


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B

C

A

1ABCABC90AC26mBC24mAB


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B

C

A

1ABCABC90AC26mBC24mAB

ABC90

RtABC,

AB2=AC2-BC2=262-242=100

AB0

AB=10(m)

AB10m


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2AC6cmBC8cmACADABAECD


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ACB90

RtABC,

AB2=AC2+BC2=62+82=100

AB=10(cm)

AE=AC=6(cm)

BE= AB- AE=10-6=4(cm)

BED = AED=ACB90

CD=DE=xcm,

DB=8-x(cm)

RtDBE,

DB2=DE2+BE2

(8-x)2=x2+42

x=3

CD=3cm.

6

10

6

4

x

x

8-x

8


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A

B

C

3S1S2S3


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A

B

C

R1,R2,R3,

S1=R12S2=R22S3=R32

RtABC,

BC2+AC2=AB2

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

R12+ R22= R32

R12+R22=R32


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1

123.AAB(3).


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C

B

B

A

A

RtABCAB15

9

12

15


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2

ABCAB=AC=10cm,

BC=6cm,

A

B

C


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AD),

A

B

C

D


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:

(1)

(2)

(3)


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