.:",
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geometria 2~ edi~ edi~ao. ao.
Raimundo NQna10 ·;-Franci,scQ Dinr Dinr Junq Junqus usha ha
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.O!":"um .O!":"um belo teerema vale uma bela ro
ta
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PREFAt:IO
'Hi,sto.ri .ri que. Contaa 'Hi,sto EllIcUdes que usasse GeomebIa.
existem
caminhos
la disci'pHna
pedht facit
Egit'O H N a o reais para -s chegar
et da
io
c.!) c.!)
E,S'te
modo organ:i-
e,le refe refere rennpostujades a' e,le bi ei criado pelo
XIX, rel,sc l,sc til' til' ,ue' ,ue'le le axlesnas, SU SUlirgiu, lirgiu, enta~ enta~ como conseqtienGeamet~:ia Nao·Eu(;lidiana, tulado de Euclides, ra leNa
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posslbjllte no p3as p3assa sa
u m ponto
reta
cons constr tru~ u~3o 3o d~ n,ovas geometdas, nu-mero ndo-se concltlsao de
to
dos.
novas concepcdes, po're'm, niiiot:inham valo aead aeadsm smlc lce, e, NaQ·. Permi'tiram as valo na Fisicaencontrou
g6gicos ito,
ge
,apli.caQao Belatli-
tr
iv e" te ri le nt nnuY nnuYel el metito t. x, pedant etq:uiS'ubtilise veulolr demontr~r lntuitton tel11es triangle est' pli(;l,s somme ux utre utress- pr,o pr,opo posi siti ti'o 'o umble caniehe, quisait fort bietl que
plus court
pa onve onvert rt
fait il en fait
ne seco second nd
cera cera la meme meme cclu cclurb rbe, e,qu qu la "Ri"Ri-en en ", st ph.s pitoyahle;, ecnclut qlle l'ensei,gI1E;lniel1t de 'la~Geometrie. etau x, qlle iu aos· ue je faisp faispass asser er de tf,~nte aos· con state exames du cette decadence. crois pas qu'il yait moment la peJine
I"ensei;gnement et 'ilraiment secm:;ldaire fe'r,art bfen d"y rennencen",
Aeharn Aeharn os.educado os.educadores, res, nestas cond,iQoes, oob. b.s( s(lr lrvac vac;a ;ao' o' aexperiencia 'que rn i. pllc pllcal al a· na melltosgeometfieo$.
Matematica Tavares,
nesta
quis quis·i ·i(f (f o-d: o-d:os os eonh eonhec ecll-
,estao pe fe t-
Froallcisco
nt
en lf Rafmul1do Nonato iniz iniz Ju quei quei:. :.ra ra Mae,xito aloaneado
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RalmllndQ , N o . . n s t o Tav,ares
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Di,zoe,moue.a
arid~, dificif
Matematica
ve ifiq ifique ue qu fsto
aprendida por.poucos. um
lnve lnve da e.
Voe!
atgumas d ec e c or o r aa- la la s s e m co c o m pr p r ee e e n dg dg - a s
Vod pl'ecisara
al ul
quese refere
dese desenv nvol ol im nt
benr benr
do aele aele inlo inlo
n:io aju-
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,~
..
NOTA NOTA
H[ST H[ST R' CA
A S M ,C O M E ~ O U
DESENVOLVER-SE
G· OME RI
N. Antig Antig
ho ea AS
Di
od
,I)
fixavam
N A C EU EU A G EO M E
da Histo;ria Cri's~o. an fazer Hvll'o mQ{lQ' Q'as as orig origel elllll d~ste mQ{l
!g~ftito., er rnai rnai pedeeoses do paia.
-.que
antes
de
sua ohra, refeee-se da Gee-metria;
Eglpto Eglpto entre entre
Se 05
h a re
.e>
Para que sabe,r como
tao
gigantes~ epoca tinham planta dessas obras,
lu-
Pat:'3 sabe sabe tud Isso.os arqu'ite't'Qs das ,piramides I'ealiiizaram d'iversas descobertas
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lA do
aspecto
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quando pernlio possuem
comum?
d a s , segmer:l'tos, saa parafelos,
pertencem
dU3S
seus seus suno sunorte rte
para para'i 'iel elas as
quand(l
tarrtbenlQ
"postulado"qlue
um
ur
apenas uma. para-
lela si,como
reta reta
quando
V·QCe
,lfamWa
de.retas paralelas"? VQCe
lades epostes de urn retangulo paraleloaf paralelogramo
as
VO£8
qu
pOll'
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notara que:
1)
dels:
3)
neres iguais.j,
Na gr
vu
derna, YOCenota, para'le,las,;
sa
ainda;,
decorac;ao
seus
~nglJlr0S
maliores
rgruais (~l\gull,os
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po ne n e ry ry c j 'i m c po
da tCandelalria domina Presiidente ,\lalrga:s, Su em 1901,. p,rohlsl;lo
1874-,
J'a,neilrio. I:ni,~
me
ostenta maier
,cor ,cores es mode modela la(l (los os s~gundQ Helt Heltor or Cord Cordov ovll ll'J 'Je. e. ,E5ta: revest:ida tUI:3S de Zeferi'no
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ANGULOS
L.eia Angulo'S.
letras
NOTA: vale
llvrc-texto,
ou
capitulo:
ct am
todos
falsa quando
se veri verifi fiqu que. e. Urn
afirma~o
rnatlea,
a)
esta in,crustada
modernos
edifidos ed ifidos
igua'is.
urna
contra-exemplo.
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ANGULOS
rcici rcici
probl probl ma
exel'clc'i'os rascunhe. 1) Ocomp1ementode mede.
h)
fg i)
obtus()s.,
2)
supiemento ahgulo
j) oi I)
ngu' ngu'ro ro
~31
replemento
lurran,guloagudo
cc
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t6) ang,uto angulos 30°. Catcula
8)
d~les
angul:o.s
400
entre
alilgl\Jl0.
dele's,
semi:'"eJa, cujaori.0 vertice gem do all'!gulo com seus rados,angulQs angul
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cr'i cr'ite te,r ,rio ios' s' de
1)
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b) 'P
um
._de tria triang ngul ulos os
1,0)
6.
esmo esmo temp tempo, o,
tdangulo
is6.sce~es;
2. ApHear caso ALA.)
b)
observanola lades
reci recipr proc ocam amen ente te
A B C . , . AD
bissetriz, DemO DemOl1 l1st stra ra que' que':. :. .. trii triin. n.9i 9iul ul tam'b~m medlana. (Su,gesUo: Apli,car case ALA.)
./J\.
'A
.ABC,
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~·B'C'
120°: Da'-seu:11i'!
B!O"
'40°, e~ d9is: tda'ng,ul,6$~sao, s.....ges"'"~o: Utiliizar caso ALA.)
COn1,primento At' De'm,onstl'ar que.: Be 17)
dos angulos
1Z>-
B'C'.
urn ponto €1,llalq,u €1,llalq,ue·ret e·ret bissetrizo bissetrizodio dio
S,.e:j'8
(AS
intenepta ""
Tra~a-se C'B'.
AC).
prol:ongam'Ento OM certa AS, ern C' Demo Demol1 l1st stra ra qure':
as: igl1 igl1ai ai sa rgua rguais is
Dois trial1gll!Jl(os
4\'0,'
iguais.
0'
1 1 : Q ) 0 1tdanguilo
2.
BB'
cc-.
Pro;l.o.nga..:seo lado SA urn cQn1primentQ At)
jlsos'celes;
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n ba ba s p o g on on a
eriYol eriYolvi vida da
envol envolyent yenteS eS
'l1J)
r:bd~' ~~{ft:ti~lltoemertorque qualquer I1nha: p : o ' g . o h a l de m e s m o s e x t r e m o s .
il'ldicar,quamlo nece~s nece~sarl arlo! o! slJ,gq slJ,gqsto stoes es paraca paracad'a d'a exerc'·c
a1UxHIar,. ·Prete,rimos
s e Q ! u in in t e s r e s u ltlt aa aa e s s I)
od tri, tri,an an.g .gu, u, Q, umal umal1g 1g.u .ulo lo ma!ior que qua1lquer do~ ,angulos lntemos
T6d;a
e,m'
n h a p o igona lconvexa enyotvida.' rQuequalquerlinhapoHgonal
'eovolVentede
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E X E 'R 'R d C I
assinalades eulas, u,)d u,)dllll res. res.
letrasmiausnecess necessari ario, o, ascon asconstr str
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SOlU(jO:
te
vocs
't
Pitagoras. 40 de
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retacoes metrica metricas,n s,n circulo circulo
1)
metro
urn etrcuto,
de um dia-
das·. Uma das eerdas mede proj proje~ e~a. a. sobr sobr igl, igl,Ja Ja 9,6c 9,6c Calicu'le cOn:'lp,r'imento dlametro bendo
Scm. Calcule cante.
passa
pelo
centro.
AC
Scme
rsnci rsnci
clrcu clrcunsc nscrr rrtaa taa
U.ma das
diametro
100m
corta
8)
circunferencia, clrc clrcUI UI,l ,lo, o, tra~ tra~a, a,mm-se se duas duas cerdas, cordas mede 150m,
se-
com-
distancia
tangel1te
suporte
tangente Sabenclo aue PM 10cm rd
igual ABC
3) Duas eordas de
ci
segmento
110)
cortam-se urna co as 9cm. calcule maior da 'outra eerd eerda, a, sace sacend ndee-se se que
um tri! tri!ng ngll lll" l"o, o, re1: re1:an angu gulo lo AC 4cm. Cal,cule passa nor AB
rai!) da tan-
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R'ln
pa
'II"!
,~
2R
V5-2
\fl'
\I
5R'VlO+2'\ji:
3R2\[i
( V
R(v;._1)
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'I 12
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--------------------------------------------------------- -------------------_
HORIZONTAlS
1)
3)
centlmetros
hexapono
re-
cerrtlmetros do apoterna
do
clreulo
de
V3)cm.
hexaqono regular
de 20 V'3cm hexaqono regUl~all'de
numeros cruzados 6)
VERTICAlS
1)
Numero de eentlmetres inscritoem
I.un cir-
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3)
c6smieo.
5)
8) 1'0/9
vexo,
numeros cruzados
VERTICAlS
1)
mentado de 2)
urn
lado.
ang,ulo. o. qJJe, qJJe, au!Ht!l ang,ul
graus, '6 i,g,uala lurt ~ngu'lo oct6gprflo reglular cenvexo, centlmetros
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circulo.
diferenca entre circunferencia
ircu ircunf nf renc rencia ia
ir
um
·.
circunferencla c'j,rcullo 6,0
une dols clrculo, ..
tr
clrculo
ircu irculo lo
desse
qualquer
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No, "Palrais Decouverte", nurrrta da.s~alas Matemae :x :x i s t valor de n, .es.c:ritQ de tecla, decirnais.
se
diam diamet et o.
Nilo peri6d peri6dica ica
dizima
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calcular
~oaocu
rteso
pareca, huer hueres es.s .s nte, nte,", ",d' d' a" ul
ro
o."dOs--tMos.s3;v@zes, jlr.ru,. ,iL,'o."dOs--tMos.s3;v@zes,
pallto risco de-seqUO",~ciente
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numeros cruzados
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poli poligo gono no regu regula la nurneros cruzados
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paralet;og!ramo
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------------~-~~~~~~~------------------------------
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