Начертательная геометрия

3. "

31

,( . 3.23).

AB//H	AB//V	AB//W

= . 3.23

' % % . / - D , ' D ( . 3.24),D ,. B D ' .

= . 3.24

32

.

, D , -+ " " D- D.

@ . 3.24, , E ( ' AB)+ K ( ' 'D). "E K. -( . 3.24, ) ) e + ) k . " NH e k. ABCD.

@ V D ) 1 2AB CD. " M , 1AB D D,V 1 AB 2 CD. AB D D.

= D % , -, .

3.7. " $% " % # "&+%, >A "

<D " D' - . @ ' - . # , " - -, ( " . @ , " ABC ( . 3.25) "P, ( " .

* D " . # - D " , " + ". = " "- .

= . 3.25

3. "

33

2. " " " ," , - .

D* " " DEK P,EK ( . 3.26). $ , " – " ked – 90 :

(ED EK) (ED // P) (EK P) (ed) (ek).

= . 3.26

0 . " DEF=90 , " 3 ( . 3.26, ). $" , ) " , ' , 3, " -3 , " def = 90 .

EF * D Q.Q 3.

Ff D – 4*. !" DEK , DE Q. " DEK" DEF, F 43. $

dek = def = 90 .

@ , , DE " DEK 3.

" *4 3.

* , ", , -( . 3.26, , ).

34

.

3.8. # ) % %& % "0 %-% ( " =+ # *:"0

# ' " D D. # -' " -" .

( D " " " .

2 . * ' "" " " " , - " , "( .

0 . * . 3.27 , -AB " " " " AB1. ( " , ".

# D AB " "H ( " ), ( . 3.28, ).

" " , "" , -H ( z A B). * B " ab0, " "H - " bab0 ( " ).

@ . 3.28, AB " " V – " .

= . 3.27

 

 

= . 3.28

3. "

35

"# "&( ) * & :"+" " *

1.& ?

2.' " ?

3.& H, V, W,( ?

4.& ) D D ' ") " ?

5.& H, V, W D ?

6.& " ) - , " " ?

7.& " " , " ) ?

8.?

9.& D

) ) " ? ) " " ?

10.% " " ) " -?

11.% " ) " " -?

12.& D H,V D- ' ?

13.& "" " ?

14.& , ) -D' -?

15.& , " -D'?

16.& - ' D' ?

17. " " "-

?

18.; )H, V , ( ?

19. " " " ? 20.& " "

' " "" H V?

4

B

D , -, D' .

4.1. #"&"'( = ) %* # "&+"& %

@ ( . 4.1) :

) , ' ( . 4.1, ); ) , ' ( ( . 4.1, ); ) D' ( . 4.1, );

") ( . 4.1, ); ) D ) " ( . 4.1, );

) ( . 4.1, ).

			= . 4.1

# " " . @- , A B ( . 4.1, ) D, -D -( . 4.1, ) . .

"' , .

, , D ( . 4.2):

PV ) P;

PH " P; PW ) P.

$ (Px, Py, Pz) - D 1 .

4. #

37

, -, ' ( . 4.2).

= . 4.2

4.2. " "/ % # "&+"& % " "&% ! " # "&+"& 0 # " +$%0

# D' :

.

.

.

, D D, D % . $ -D , . 4.1, 4.2, . 4.3.

, D 5-, 1 % ( . 4.4). , % -D , 1 % ( . 4.5).

' - ' , " ,. * , ' ( . 4.4), , " ABC – " abc ) a b c – D -( ). " A1B1C1,' ( . 4.5), D -: " a1b1c1 , ) a 1b 1c 1 .

38

.

= . 4.3

= . 4.4

= . 4.5

+ . ,, D -.

+ , , % .

$ -*?- ! $ P(ABCD) H

( . 4.6)

= . 4.6

4. #

39

B $ -*?- ! $ Q(ABCD) V

( . 4.7)

= . 4.7

#$ -*?- ! $ T(ABCD) W

( . 4.8)

= . 4.8

+ - , . 6 -. ! --.

D' D :, ) " , -

40

.

, ( - D D' .

+ , , -. ( D' ).

$ ! $ P(ABCD) II H ( . 4.9)

= . 4.9

B $ ! $ Q(ABCD) II V ( . 4.10)

= . 4.10