1

6

3.2 : 1 6.1 : 1 2 6.2 : 1 6.3 : 1 6.4 : 1 2 6.5 : 1

1.

2.

6.1 (4 ) 6.2 (4 ) 6.3 (2 )

?

2 .2

. 15

66..11

: 1.

2.

/ : 1. 2. 3. 4. 5. 6.

: 1. 2. 3. 4. 5. 6.

MATH

Series

6 3

. 15

ABC ACB

a b c ..

1.

a, b c

a b c a2 b2 c2 a2 + b2 c2 a2 + b2 1) 4 3 2) 6 8 3) 2.4 3.2

1)

2) 3)

C A

B

a

b

c

6.1 :

4 .2

. 15

ABC ACB

a b c

c2 = a2 + b2

1.

1) 2)

6.2 :

C A

B

a

b

c

z x

y

p n

m

6 5

. 15

3) 4)

5) 6)

2.

1) 3, 4 2) 9, 12

1

c2 = a2 + b2

= 42 + 32 = 16 + 9 = 25

c = 5 5

r t

8

7

12

a

26 24

c

15

b 9

A

C B a = 4

c = ? b = 3

6 .2

. 15

2

c2 = a2 + b2

= 62 + 82 = =

c =

3

c2 = a2 + b2 = = =

c =

1. 2.

x2 = 52 + 122 x2 = 0.52 + 1.22 x2 = 25 + 144 x2 = .. x2 = 169 x2 = .. x = 13 x = ..

6.3 :

A

C B a = 6

c = ? b = 8

A

C B a = 15

c = ? b = 8

12

5 x

0.5

1.2 x

6 7

. 15

3. 4.

5. 6.

x2 = 1.22 + 1.62 = 1.44 + 2.56 = 4.00 x = 2

4 b

c2 = a2 + b2

b2 = c2 a2

= 132 52 = 169 25 = 144

b = 12 b 12

24 7

x

1.2 1.6

x

A

C B a = 5

c = 13 b = ?

8

15 x 0.3

0.4

x

8 .2

. 15

5

c2 = a2 + b2

a2 = c2 b2 =

= =

a = .

1. 2.

x2 = 202 122 x2 = 3.92 1.52 x2 = 400 144 x2 = .. x2 = 256 x2 = .. x = 16 x = ..

12 + 20 + 16 = 48 =

A

C B a = ?

c = 10 b = 6

6.4 :

12

20 x 3.9

1.5

x

()

6 9

. 15

3. 4.

5. 6.

3,000

8

15 x 0.3

0.4

x

15

12 x 3.9

x 1.5

10 .2

. 15

2

ABC ACB a b c

c2 = a2 + b2 a2 = c2 b2 b2 = c2 a2

C

A B

C A

B

a

b

c

6 11

. 15

1. a = 7, b = 24 2. a = 30, c = 34

3. a = 21, c = 35 4. a = 18, b = 24

5. a = 28, c = 35 6. a = 22, b = 120

6.5 :

a

b

c

12 .2

. 15

66..22

:

1. 2.

/ : 1. 2. 3. 4. 5. 6.

: 1. 2. 3. 4. 5. 6.

MATH

Series

6 13

. 15

1. a, b c

a b c a2 + b2 c2 a2 + b2 c2

1) 6 8 10 36 + 64 100 2) 6 12 13 3) 9 12 15 4) 7 15 14 5) 6 6.25 7.25 6) 1.4 3.6 4 7) 2.5 6 6.5 8) 4 6.5 8.5

2. 1) a = 3, b = 4 c = 5

a2 = . b2 = . a2 + b2 = c2 = . a2 + b2 c2

2) a = 6, b = 8 c = 10 a2 = . b2 = . a2 + b2 = c2 = .

6.6 :

14 .2

. 15

a2 + b2 c2

3) a = 5, b = 5 c = 10 a2 = . b2 = . a2 + b2 = c2 = . a2 + b2 c2

4) a = 6, b = 5 c = 11 a2 = . b2 = . a2 + b2 = c2 = . a2 + b2 c2

ABC a, b c c2 = a2 + b2

ABC c

: :

6 15

. 15

26 27 1 ABC ABC CDB

BC2 = CD2 + DB2 = 122 + 162 = 144 + 256

BC2 = 400 ADC

AC2 = CD2 + AD2 = 122 + 92

= 144 + 81 AC2 = 225

AC2 + BC2 = 225 + 400 = 625

AB2 = (AD + DB)2 = (9 + 16)2 = 625

AB2 = AC2 + BC2 ABC ACB

A B D 9 16

12

C

16 .2

. 15

1. 1) 6, 8, 10 2) 4, 6, 8

a = 6 a2 = 36 b = 8 b2 = 64 c = 10 c2 = 100 a2 + b2 = 36 + 64 = 100 a2 + b2 = c2

3) 8, 10, 12 4) 8, 17, 15

5) 1, 4, 5 6) 0.3, 0.4, 0.5

6.7 :

6 17

. 15

2. 1)

2)

C

A

B 25 E

60

144

A

B C D 18 32

24

18 .2

. 15

66..33

:

1.

/ : 1. 2. 3. 4. 5. 6.

: 1. 2. 3. 4. 5. 6.

MATH

Series

6 19

. 15

1

1. CE AD E

2. ABCD DEC 3. EC = 3 ED = 4 4. DC2 = 32 + 42

= 9 + 16 = 25 DC = 5

5 2 BD

AD = BD = 8 BD2 = AD2 + AB2 = .. = .. = .. BD = ..

BD ..

A B

C

G H D

E F

6

8

4

3

7

A B

C

D

3

x

3

4

A B

C

D

3

x

3

E

20 .2

. 15

1. DE

2. ABCD

6.8 :

C

E D

B 11

6

13

3

5 10

x A B

C D

6 21

. 15

3. 25 24

4. C ABC A C 160 B C 128 A B

24 25

A

B C

A

B

C 160

128

22 .2

. 15

5. 10 8

3 ABC 21 72 75 ABC

a = 21 b = 72 c = 75

a2 = 441 b2 = 5,184 c2 = 5,625

a2 + b2 = 441 + 5,184 = 5,625 c2 = a2 + b2 ABC

4 ABC CD AB D ABC AC = 13, BC = 15 CD = 12

DCB DB2 = BC2 DC2

= 152 122 = 225 144 = 81

10 8

A

B

C

75 21

72

A

B C

D 13

15

12

6 23

. 15

DB = 9 ADC AD2 = AC2 CD2 =

= AD2 = AD =

AC2 + CB2 = 132 + 152 = =

AB2 = (5 + 9)2 = =

AB2 AC2 + CB2

ABC AB2 AC2 + CB2

1. ABC CD AB D ABC 1) AC = 10, BC = 17 CD = 8

6.9 :

A

B C

D 13

15

12

24 .2

. 15

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

6 25

. 15

2. ABC AB = 63 , AC = 60 BC = 87 AD ()

... ... ... ... ... ... ... ... ...

3. AB = 21 , BC = 28 , CD = 7.2 DE = 9.6 AE = 37 ADE

... ... ... ... ... ... ... ... ...

A

B C D

60 63

87

A

B D C

E

37

21

28 7.1 9.6

26 .2

. 15

ABC 1. c2 < a2 + b2 ACB 90 90 2. c2 > a2 + b2 ACB 90 90

A B

C

c

a b