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a b
c
a, b c
c a b
n
c
a b
a b c
c
a b)
[7]
a, b c
a b
a, b c
a b 90°
Euclid's Elements [8]
ABC a,b c
a b
a b
c
a b
,
c
1.2.
a, b c
c a
b
n
a
b c
--
ABC AĈB
a , b c A
, B C
a , b c
ABC c a
b ABC
c
ABC
c
a b
c a b
ABC
a , b c c2 = a2 + b2
ABC
c
"
c2
= a2
+ b2
a b
c
ABC
C
AB AC
BC
a A
b B, c
C c
5
a,b
3 4
1.
a 9 b 16
2.
2
3.
25 = 9 + 16
4.
5. 4
1) 5
8 10
( 17
2) 8 6
( 10
3) 2
10
7 14
25
4)
5:5:10
5) 2
15 25
( 22
6) 2
9
12
( 24
7) 7
25 ( 84
8) ABCD BC = 10 CD = 5
AD = 26 ? ( 48 24
9)
1 15
12
9
10) 10 4 8
3 6
25
11) 6
8 ( 20
12) 4
6 4
10
13) 10
15 18
( 17
14) 13
5 ( 12
15) 26
24 ( 10
16) 9 12
15
17) 10.30 170
1 5
( 13
18)
157 227
19) 15 8
17
20) 100
24,600
1. 3,4,5
2. 5,12,13
3. 7,24,25
4. 8,15,17
5. 9,40,41
6. 11,60,61
7. 12,35,37
8. 20,21,29
(3,4,5) (6,8,10) (9,12,15) (12,16,20) (15,20,25) (18,24,30)
(3,4,5)x2 = (6,8,10)
(3,4,5)x3 = (9,12,15)
(3,4,5)x4 = (12,16,20)
(3,4,5)x5 = (15,20,25)
(3,4,5)x6 = (18,24,30)
2
1.2
"
c2
= a2
+ b2
a b
c
ABC
C
AB AC
BC
a A
b B, c
C c
5
a,b
3 4
1.
a 9 b 16
2.
2
3.
25 = 9 + 16
4.
5. 4
1) 5
8 10
( 17
2) 8 6
( 10
3) 2
10
7 14
25
4)
5:5:10
5) 2
15 25
( 22
6) 2
9
12
( 24
7) 7
25 ( 84
8) ABCD BC = 10 CD = 5
AD = 26 ? ( 48 24
9)
1 15
12
9
10) 10 4 8
3 6
25
11) 6
8 ( 20
12) 4
6 4
10
13) 10
15 18
( 17
14) 13
5 ( 12
15) 26
24 ( 10
16) 9 12
15
17) 10.30 170
1 5
( 13
18)
157 227
19) 15 8
17
20) 100
24,600
1. 3,4,5
2. 5,12,13
3. 7,24,25
4. 8,15,17
5. 9,40,41
6. 11,60,61
7. 12,35,37
8. 20,21,29
(3,4,5) (6,8,10) (9,12,15) (12,16,20) (15,20,25) (18,24,30)
(3,4,5)x2 = (6,8,10)
(3,4,5)x3 = (9,12,15)
(3,4,5)x4 = (12,16,20)
(3,4,5)x5 = (15,20,25)
(3,4,5)x6 = (18,24,30)
2
1.2
ทฤษฎีบทพีทาโกรัส

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ทฤษฎีบทพีทาโกรัส

  • 2. c a b n c a b a b c
  • 4. [7] a, b c a b a, b c a b 90° Euclid's Elements [8] ABC a,b c a b a b c
  • 7. a b c -- ABC AĈB a , b c A , B C
  • 8. a , b c ABC c a b ABC c ABC c a b c a b ABC a , b c c2 = a2 + b2 ABC c
  • 10. ABC C AB AC BC a A b B, c C c 5 a,b 3 4 1. a 9 b 16 2. 2 3. 25 = 9 + 16 4.
  • 11. 5. 4 1) 5 8 10 ( 17 2) 8 6 ( 10 3) 2 10 7 14 25 4) 5:5:10 5) 2 15 25 ( 22 6) 2
  • 12. 9 12 ( 24 7) 7 25 ( 84 8) ABCD BC = 10 CD = 5 AD = 26 ? ( 48 24 9) 1 15 12 9 10) 10 4 8 3 6 25 11) 6 8 ( 20 12) 4 6 4 10 13) 10 15 18
  • 13. ( 17 14) 13 5 ( 12 15) 26 24 ( 10 16) 9 12 15 17) 10.30 170 1 5 ( 13 18) 157 227 19) 15 8 17 20) 100 24,600
  • 14. 1. 3,4,5 2. 5,12,13 3. 7,24,25 4. 8,15,17 5. 9,40,41 6. 11,60,61 7. 12,35,37 8. 20,21,29 (3,4,5) (6,8,10) (9,12,15) (12,16,20) (15,20,25) (18,24,30) (3,4,5)x2 = (6,8,10) (3,4,5)x3 = (9,12,15) (3,4,5)x4 = (12,16,20) (3,4,5)x5 = (15,20,25) (3,4,5)x6 = (18,24,30) 2 1.2
  • 16. ABC C AB AC BC a A b B, c C c 5 a,b 3 4 1. a 9 b 16 2. 2 3. 25 = 9 + 16
  • 17. 4. 5. 4 1) 5 8 10 ( 17 2) 8 6 ( 10 3) 2 10 7 14 25 4) 5:5:10 5) 2 15 25 ( 22
  • 18. 6) 2 9 12 ( 24 7) 7 25 ( 84 8) ABCD BC = 10 CD = 5 AD = 26 ? ( 48 24 9) 1 15 12 9 10) 10 4 8 3 6 25 11) 6 8 ( 20 12) 4 6 4 10
  • 19. 13) 10 15 18 ( 17 14) 13 5 ( 12 15) 26 24 ( 10 16) 9 12 15 17) 10.30 170 1 5 ( 13 18) 157 227 19) 15 8 17 20) 100 24,600
  • 20. 1. 3,4,5 2. 5,12,13 3. 7,24,25 4. 8,15,17 5. 9,40,41 6. 11,60,61 7. 12,35,37 8. 20,21,29 (3,4,5) (6,8,10) (9,12,15) (12,16,20) (15,20,25) (18,24,30) (3,4,5)x2 = (6,8,10) (3,4,5)x3 = (9,12,15) (3,4,5)x4 = (12,16,20) (3,4,5)x5 = (15,20,25) (3,4,5)x6 = (18,24,30) 2 1.2