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บทกลับของทฤษฎีพิทาโกรัส PowerPoint PPT Presentation


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สรุป. ถ้า c 2 = b 2 + b 2 แล้ว ABC เป็น มุมฉาก. ในรูป ใดๆ ที่มีด้านยาว (3 , 4 , 5) (5 , 12 , 13) (7 , 24 , 25) เป็นด้านของ มุมฉากเสมอ. จำ. บทกลับของทฤษฎีพิทาโกรัส.

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บทกลับของทฤษฎีพิทาโกรัส

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5952691

c2 = b2 + b2 ABC

(3 , 4 , 5) (5 , 12 , 13) (7 , 24 , 25)

: ABC a , b c c2 = a2+ b2 ABC c


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144 164

64 52

=

=

1

1) 6 , 8 , 10

3) 8 , 10 , 12

2) 4 , 6 , 8

c2 = a2 + b2

c2 = a2 + b2

c2 = a2 + b2

102 = 62 + 82

122 = 82 + 102

82 = 42 + 62

100 = 36 + 64

144 = 64 + 100

64 = 16 + 36

100 = 100


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36 17

0.25 0.25

=

=

4) 8 , 17 , 15

5) 1 , 4 , 6

6) 0.3 , 0.4 , 0.5

c2 = a2 + b2

c2 = a2 + b2

c2 = a2 + b2

0.52 = 0.32 + 0.42

172 = 82 + 152

62 = 12 + 42

0.25 = 0.09 + 0.16

289 = 64 + 225

36 = 1 + 16

289 = 289


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ABC

A

24

32

18

B

C

D

ABC

2500

2500=

2

2.1

AB2 = AD2 + BD2

AB2 = 242 + 182

AB2 = 576 + 324

= 900

AC2 = AD2 + DC2

AC2 = 242 + 322

AB2 = 576 + 1024

= 1600

BC2 = AB2 + AC2

(18+32)2 = 302 + 402

502 = 900 + 1600


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A

60

144

25

B

C

D

A

A

A

D

C

B

C

B

D

AB2 +

BC2 =

AC2

ABC

AB2

= 625 + 3600

AC2

= 20736 + 3600

(25 + 144)2

= 4225

= 24336

= 652 + 1562

28561

28561

=

AB

AC

= 65

= 156


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C

13

15

12

A

D

B

AC2 +

AC2 +

AB2 =

AB2 =

BC2

BC2

BC2 -

169-

152 -

225-

AC2 -

132 -

BD2 =

AD2 =

AD2 =

BD2 =

AD2 =

BD2 =

144

CD2

144

122

CD2

122

132 +

(5+9) 2 =

152

169+

196

225

=

ABC CD AB D ABC

3

1) AC = 13 , BC = 15 CD = 12

= 81

= 25

ABC


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C

10

17

8

A

D

B

AC2 +

AC2 +

AB2 =

AB2 =

BC2

BC2

102 -

172 -

BC2 -

289-

100-

AC2 -

BD2 =

BD2 =

BD2 =

AD2 =

AD2 =

AD2 =

82

CD2

64

64

CD2

82

102 +

(15+6) 2 =

172

100+

441

289

=

2) AC = 10 , BC = 17 CD = 8

= 225

= 36

ABC


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42 -

BD2 =

2.42

C

3

4

2.4

A

D

B

(3.2+1.8) 2 =

32 +

32 -

AD2 =

42

2.42

AC2 +

AB2 =

BC2

AC2 -

BC2 -

AD2 =

BD2 =

CD2

CD2

9-

9+

AD2 =

25

5.76

16

=

AC2 +

AB2 =

BC2

2) AC = 3 , BC = 4 CD = 2.4

16-

BD2 =

= 10.24

5.76

= 3.24

ABC


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ABC AB = 63 AC = 60 BC = 87 AD (

4

A

63

60

B

D

C

87

ABC

1

60

63

1

x

x

2

x

x

2

1890=

2

1890

1

x

87

AD

x

x

87

2

BC2 = AB2 + AC2

872 = 632 + 602

7569 = 3969 + 3600

= 7569

=

ABC=

= 1890

= 43.45

AD =


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AB = 21 , BC = 28 , CD = 7.2 DE = 9.6 AE = 37 ACE

5

A

37

E

21

9.6

B

D

C

7.2

28

CDE

ACE

ABC

1369

= 1225

+ 144

CE2 = CD2 + DE2

CE2 = 7.22 + 9.62

CE2

= 51.84

+ 92.16

= 144

AC2 = AB2 + BC2

AE2 = AC2 + CE2

AC2 = 212 + 282

372 = 352 + 122

AC2

= 1225

= 1369

= 441

+ 784

ACE


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A

37

E

35

12

B

D

C

1

ACE=

12

35

1

x

x

2

x

x

2

=

ACE=

210


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a2 = 102 - 82

8

10

a

8 10

6

a

a2 = 100 - 64

= 36

= 6


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7 12 15 15

7

C

D

15

7

A

12

B

193

225

ABC

152= 122 + 72

225 = 144 + 49

ABC

BD AC AC BD


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