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Retrieved from Digital Repository at Srinakharinwirot University http://kids-d.swu.ac.th

5

1. 2.

A

B

B A

5.1

5.1.1) A B

A z

z B A B AB AB


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-133-

1

1. 1

1 .........................

2. 2

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

3. 2

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


1

-134-

1.

1) 2) 3) 4)

5) 6) 7) 8)

9) 10) 11) 12)

13) 14) 15)

16) 17) 18) 19) 20)

2

1) ......................................................................... 2) ........................................................................................... 3) ............................................................................................ 4) .....................................................................................


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-135-

5.1.2)

A B AB AB BA BA CD CD EF EF

GH GH

AB ) AB measure of AB 5 m = 5 . AB = 5 .

(ABm ( )ABmAB AB

( )AB AB + CD + CD

AB ( )ABmAB CD ( ) ( )CDm+ABm

AB

H

G

F

E

D C

B

A

1)

2) 2


1

-136-

3


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-137-

5.1.3)

B B

A A A B AB BA

B B BA AB

1) B AB AAB

5.1.4)

A

R () C ABC B BC B

BA ABC A

() DEF ED E

FED DEF EF

RQP PQR () PQR QP QR B

() () B P Q


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ABC DEF

C

A

B D F

E ABC

ABC 30 m = 30 ( )CBAm ( )ABCm

( )CBA AB CD E

m = m ( )DEA ( )BECA = m ( )( )CEAm BED DEA BEC

C D CE BEAB


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1. 2. 3. 4. 5.

5.2

, , ,

5.2.1) 1 AB XY AB

A

Y

1) XZ AB

2) X AB Y

XZ XYAB

AB XY

XY AB XY


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1. AB

A B

CD CD A B

1.1............................................................................................................................................................................................................................................................................................................... 1.2............................................................................................................................................................................................................................................................................................................... 2. a , b c 3

a b c

ABC a , b c

1).................................................................................................. 2) ................................................................................................. 3) ................................................................................................. 4) ................................................................................................. 5)................................................................................................... 6) ..................................................................................................


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3. a , b , c d 4 d

ABCD a , b , c d 1) ................................................................................................................................... .......................................................................................................................................................... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .......................................................................................................................................................... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... ..........................................................................................................................................................


1

-142-

5.2.2)

2 AB

B

1) A B AB M N

2) MN AB O O 2 AO = OB AB

O AO = OB AB


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5) ..............................................................................................

G H

GH 8 2)

M N 1) .............................................................................................. 2) .............................................................................................. 3) .............................................................................................. 4) .............................................................................................. 5) ..............................................................................................

MN 4 1)


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5.3

3 C m ( ) ( )ZYX B m=CB ZYA A X ZYX

1) BC

2) Y YX YZ M N

3) B YM BC O 4) O MN P 5) BA P m ( ) ( )ZYXm=CBA

O

P

C

X

M

B N Z Y


1

-145-

1. 2.

5.4

4 T 2 AC C TA 1) A M

N AC AT

2) M N O AO

T 2 AO AC ( ) ( )TAOm=OACm


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-146-

6

CBA ZYX

X

Y Z

1) ......................................................................................................

2) ...................................................................................................... 3) ...................................................................................................... 4) ...................................................................................................... 5) ......................................................................................................

2) CBA ZYX

X

Y Z

1) .....................................................................................................

2) ..................................................................................................... 3) ..................................................................................................... 4) ..................................................................................................... 5) .....................................................................................................


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3) MNO 4 M

N O

1) ......................................................................................................

2) ...................................................................................................... 3) ...................................................................................................... 4) ...................................................................................................... 5) ...................................................................................................... 6) ......................................................................................................

4) ABC 8 A

C

B 1) .....................................................................................................

2) ..................................................................................................... 3) ..................................................................................................... 4) ..................................................................................................... 5) ..................................................................................................... 6) ..................................................................................................... 7) ..................................................................................................... 8) .....................................................................................................


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5.5 60 5 J 60=NA

Y X

Z XZ XY

APAQ PQ

P

N

J

1) AJ

2) A AJ P 3) P AP Q 4) AN Q m ( )AJ 60=N

60


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-149-

7

1) 30 1) ..........................................................................................................

2) .......................................................................................................... 3) .......................................................................................................... 4) .......................................................................................................... 5) .......................................................................................................... 6) ..........................................................................................................

2) 120 1) .........................................................................................................

2) ......................................................................................................... 3) ......................................................................................................... 4) ......................................................................................................... 5) ......................................................................................................... 6) .........................................................................................................


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5.6 90 6 P PQR 90=RQ 1) PX Q PX

2) Q PX M N 3) M N R 4) QR P PQR 90=RQ

P Q M N X

180 2 PQX


1

-151-

8

5.7

1) .........................................................................................................

2) ......................................................................................................... 3) ......................................................................................................... 4) ......................................................................................................... 5) ......................................................................................................... 6) .........................................................................................................

3) .......................................................................................................... 4) .......................................................................................................... 5) ..........................................................................................................

2) 270

1) ..........................................................................................................

45

1)


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5.7.1) 7 O AB AB O AB AB 1 2

X M M B B A A P

O

1) O O AB

X Y ( 2 P X Y )

AB AB

2) X Y Q 3) OQ AB AP M OM O AB

5.7.2) 90


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1

1) ......................................................................................................... 2) ......................................................................................................... 3) .

1) ......................................................................................................... 2) ........................................................................................................ 3) ........................................................................................................ 4) ........................................................................................................

ABC

a b

a


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d c

3) a , b c a , b c

1) .........................................................................................................

2) ........................................................................................................ 3) ........................................................................................................ 4) ........................................................................................................ 5) ........................................................................................................

4) a , b , c d

a , b , c d

a b

a

c

b 1) .........................................................................................................

2) ......................................................................................................... 3) . 4) . 5) . 6) .


1

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2

1)

1) .........................................................................................................

2) ......................................... ............................................................... 3) ........................................................................................................ 4) ........................................................................................................ 5) ........................................................................................................

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

2) a b ABC AB a

b=ABC=BAC

1) ........................................................................................................

2) ........................................................................................................ 3) ........................................................................................................ 4) ........................................................................................................ 5) 6)

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

A B

b

C

D

a

CBA CBD


1

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2 ()

a 3) ABCD a b c

ACAB CB

1) ..........................................................................................................

2) ......................................................................................................... 3) ......................................................................................................... 4) ......................................................................................................... 5) .........................................................................................................

4) a

ABC AB a ONM=BC , ZX=AA YBC

1) .........................................................................................................

2) ......................................................................................................... 3) ......................................................................................................... 4) ......................................................................................................... 5) ......................................................................................................... 6) .........................................................................................................

b

c

M

N O X

Y Z


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5) C BA 1) ..........................................................................................................

2) ......................................................................................................... 3) ......................................................................................................... 4) ......................................................................................................... 5) .........................................................................................................

6) C BA

1) .......................................................................................................

2) ........................................................................................................ 3) ........................................................................................................ 4) ........................................................................................................ 5) ........................................................................................................ 6) ........................................................................................................ 7) ........................................................................................................ 8) ........................................................................................................

A

B

A

C

B C


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3

1) TOP 60 2) AOM 120 3) 30 4) 45 BEN KIT 5) LEK 15 6) HAM 22.5 7) AU 150 8) YOT 240 M 9) SAN 270 10) NED 300


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11) WA 135 12) TI 292.5 S K

13) MAY 105 14) OIL 75 15) GEM 225 16) CHU 165 17) PUN 247.5 18) SOI 330

() ABC B () DEF E

ABC DEF = 2 ()

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