GEOMETR IA -MARZOABRILMAYO-MAYO SACO OLIVEROS PRIMARIA LOCUTORIO REN@TRIX CEL :992444616
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
GEOMETRÍA HISTORIA DE LA GEOMETRÍA
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SACO OLIVEROS
GEOMETRIA
6º PRIM.
ELEMENTOS GEOMÉTRICOS Idea de punto.-
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Segmento de Recta.SACO OLIVEROS
GEOMETRIA
6º PRIM.
Es %a p$ci( *& $&c,a c'p$&(*i*a &(,$& *s p#(,s.
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OPERACIONES CON SEGMENTOS SACO OLIVEROS
GEOMETRIA
6º PRIM.
S( %as *i&$&(,&s p&$aci(&s #& s& p#&*&( $&a%i3a$ c( %s (>'&$s $&a%&s #& $&p$&s&(,a( a %as %("i,#*&s *& %s s&"'&(,s. E#emp"o$% &.
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A B = A D - B
BC = AC - AB
A B = 2 8 - 1 5
BC = 19 - 13
A B = 1 3
BC = 6
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B
M
4= 12
C
BC = AC – AB
BM = 2B
B C = 4= < 12
BM = 14
B C = 2B
2
X = 1 2 1 4 X = 2 6
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
GEOMETRÍA
CAYLEY, ARTHUR
A$,7#$ Ca%& (aci* &( A". 16 1B21 '#&$, &( E(&. 26 1B9D #& #( 'a,&'),ic i("%5s #i&( c(,$i-# "$a(*&'&(,& c( &% a*&%a(, *& %a 'a,&'),ica p#$a. S& "$a*# &( %a 1B42F T$i(i, C%%&"& Ca'-$i*"& 5% ')s ,a$*& &(,$ &( %&&s ps,&$i$'&(,& #& a*'i,i* &( %a L(*( ?a$ 1B49F. Ca%& *&sa$$%% %a ,&$+a *& %a i(a$ia(3a a%"&-$aica s# *&sa$$%% *& %a "&'&,$+a (*i'&(si(a% 7a si* ap%ica*a &( %a +sica a% &s,#*i *&% &spaci,i&'p c(,i(#. S# ,$a-a &( %as MATRICES *&% )%"&-$a si$i c' #( #(*a'&(, pa$a %a MECHNICA CUHNTICA %a c#a% #& *&sa$$%%a*a p$ &$(&$ &is&(-&$" &( 192D. Ca%& ,a'-i5( s#"i$i #& %a GEOMETRJA EUCLI;IANA NOEUCLI;IANA s( ,ips &sp&cia%&s *& "&'&,$+a. U(i %a GEOMETRJA PROKECTIVA %a c#a% *&p&(*& *& %as p$pi&*a*&s i(a$ia(,&s *& %as 8"#$asF %a "&'&,$+a '5,$ica *&p&(*i&(,& &( ,a'as *& )("#%s %("i,#*&s *& %+(&asF. S& p#-%ica$( %s ,$a-as 'a,&'),ics *& Ca%& &( Ca'-$i*"& 1BB9 9BF.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
!AR OR/E0A/O Y !RO/12TO 2ARTESIA0O U( pa$ $*&(a* s& si'-%i3a:
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E#emp"o$% &3 a%%a$&'s &% p$*#c, ca$,&sia(. A = { $}
B = { %& ' }
A × B = { ( $%) ( $& ) ( $' ) ( %) ( & ) ( ' ) }
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A
B % $
& ' SACO OLIVEROS
GEOMETRIA
6º PRIM.
/iagrama carte$iano B ' & % A $
/iagrama Ta6u"ar B
%
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'
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($ ) % *
($ ) &*
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Si: C = { 1@ 4}
D = { 1@ B@ 2/}
a%%&'s: C×D={ D× E = {
E = { 1@ 2}
Si: E = { B@ 1=@ 12}
! = { 4@ D@ 6}
a%%&'s: E × ! = { !× E ={
C× E ={
GEOMETRIA
SACO OLIVEROS
GEOMETRIA
6º PRIM.
RELA2IO0ES BI0ARIAS T*a $&%aci( -i(a$ia ,i&(& #( c(#(, *& pa$,i*a #( c(#(, *& %%&"a*a c( #(a p$pi&*a* P x # F &(,$& A B. Pa$a *&8(i$ #(a $&%aci( -i(a$ia R &s (&c&sa$i c(c&$ #(a p$pi&*a* P x # F &(,$& A B % #& $i"i(a #( "$a s#-c(#(, *& A BF. Pa$a ,* pa$ $*&(a* x # F p&$,&(&ci&(,& a% "$a #& c#'p%& %a p$pi&*a* P x # F s& *i$) #& x &s,) &( $&%aci( c( # a*&')s # &s %a i'a"&( *& x . E#emp"o%
;a*s: E = { 12Q}
! = { 12Q4D6}
R : E → !
;&8(i*a c' ........ %a 'i,a* *& ........ E% "$a s&$): + = { ( 1@ 2) ( 2@ 4) ( Q@ 6) } Ta 6 "a d e d o 6 "e e n tra d a 1 1 2
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3 SACO OLIVEROS
GEOMETRIA
6º PRIM.
/OMI0IO Y RA0GO /E 10A RELA2I70 BI0ARIA /ominio de R% Es &% c(#(, $'a* p$ %s p$i'&$s c'p(&(,&s *& %s pa$&s x # F #& p&$,&(&3ca( a %a $&%aci(. E ( x @ # F
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E s %a 2 * a . c ' p ( & ( , &
R = { ( 22) ( QQ) ( 44 ) } ;'( R ) = { 2Q4}
Ra("( R ) = { 2Q4}
S = { ( 24 ) ( QQ) ( 42) } ;'( S ) = { 2Q4}
&.
Ra("( S) = { 2Q4}
;a*s %s c(#(,s: P
=
{ 1@ 2@ Q@ 4}
Q = { @ "}
a%%a$: PX (.
O-s&$a &% c(#(,: A × B = { ( @ D) @ ( @ 6) @ ( @ / ) @ ( "@ D) @ ( "@ 6) @ ( "@ / ) }
Esc$i-& %s &%&'&(,s *&% c(#(, A ? ).
;a*s %s c(#(,s: A × B = { @ "@ ,@ -}
. = { 1@ 2@ Q}
SACO OLIVEROS
GEOMETRIA
6º PRIM.
a%%a$: S XT
*.
;a*s %s c(#(,s: R = { 1@ 2@ Q}
a%%a$: Q
+.
Q = { D@ 6} ×
R
a%%a &% p$*#c, ca$,&sia( *& %s c(#(,s: S = { 1@2@Q@B@1=} . = { D@/@12@16}
a%%a %s pa$&s $*&(a*s *& S × ,a%&s #& a'-as c'p(&(,&s s&a( i'pa$&s.
,.
a%%a &% p$*#c, ca$,&sia( *& %s c(#(,s: S = { 1@2@Q@B@1=} . = { D@/@12@16}
a%%a %s pa$&s $*&(a*s *& S pa$&s.
×
,a%&s
#& a'-as c'p(&(,&s s&a(
SACO OLIVEROS
GEOMETRIA
.
6º PRIM.
a%%a &% p$*#c, ca$,&sia( *& %s c(#(,s: S = { 1@2@Q@B@1=} . = { D@/@12@16}
a%%a %s pa$&s $*&(a*s *& S × &( %s #& %a s&"#(*a c'p(&(,& s&a 'a$ #& %a p$i'&$a
.
a%%a &% p$*#c, ca$,&sia( *& %s c(#(,s: S = { 1@2@Q} . = { 4@D@6}
a%%a %s pa$&s $*&(a*s *& S T &( %s #& %a p$i'&$a s&"#(*a c'p(&(,& s#'&( /
8.
O-s&$a &% c(#(,: C × D = { ( 1@ x ) @ ( 1@ #) @( 2@ x ) @ ( 2@ #) @ ( Q@ x ) @ ( Q@ # ) @ ( 4@ x ) @ ( 4@ # ) }
Esc$i-& %s &%&'&(,s *&% c(#(,: C = { ................................................} D = { ................................................} SACO OLIVEROS
GEOMETRIA
6º PRIM.
&9. A c(,i(#aci( s& ,i&(& ,$&s c(#(,s i(c'p%&,s: A = { -}
B = { }
A × B = { ( " ) ( " o ) ( " / ) ( - ) ( - o ) ( - ) }
C'p%&,a %s ,$&s c(#(,s.
&&. Si: A = { 2@ Q@ 4} a%%a$ A ?
B = { 1@ 2}
&(. S&a: A = { 2@4@6} B = { Q@4@D}
R2 0 &s
'a$ #& "
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0
RR2F
0
SACO OLIVEROS
GEOMETRIA
&.
6º PRIM.
S&a: B = { Q@D@/} C = { 2@4@6}
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a 9
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0 RR2F 0 (.
Si: A = { 2@Q@4} B = { B@12@1D}
R&%aci( R0 &s *iis$ *& " a%%a$: R={ DERF = { RERF = {
).
R = { ( Q@ Q) @ ( 4@ 2) @ ( 4@ Q) @ ( D@ 2) @ ( D@ Q) @ ( D@ 4 ) }
a%%a$: SACO OLIVEROS
GEOMETRIA
6º PRIM.
DERF = { RERF = {
SACO OLIVEROS
GEOMETRIA
6º PRIM.
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SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
GEOMETRÍA CANTOR, GEORG
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SACO OLIVEROS
GEOMETRIA
6º PRIM. (NGULOS Es %a #(i( *& *s $as #& ,i&(&( #( 'is' $i"&(.
E%&'&(,s: aF La*s ⇒ OAOB -F V5$,ic& ⇒ O
A O B
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S& c%asi8ca( &(: a3
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c3 > ngu"o o6tu$o
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' i* & & ( , $& 9 = 1 B =
' i* & 1 B =
M E P
B
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+
SACO OLIVEROS
GEOMETRIA
(.
!or "a po$ici'n de $u$ "ado$ S& c%asi8ca( &(:
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6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
<.
Teorema$
&.
La s#'a *& %as '&*i*as *& %s )("#%s CONSECUTIVOS $'a*s a%$&*&*$ *& #( 'is' 5$,ic& a #( 'is' %a* *& #(a $&c,a &s 1B=º
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6º PRIM.
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SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
RECTAS PARALELAS CORTADAS POR UNA RECTA SECANTE I.
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).
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SACO OLIVEROS
GEOMETRIA &. (. ). *. +.
6º PRIM.
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GEOMETRIA
6º PRIM.
SACO OLIVEROS
GEOMETRIA
6º PRIM.
SACO OLIVEROS
